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A Stacks Project for pluripotential theory

5,957 entries · 25 chapters · 491 sections · 4 sources

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Table of contents

Chapter 1. Conventions358B9256A93C

1.1 ConventionsDE921263

Chapter 2. Measures, distributions, and convergence23B07AA86991

2.1 Measures and distributionsB288B328
2.2 Radon measures and integrationDAFA3E4936D2
2.3 Positive linear functionalsCBAFDF86F98D
2.4 Test functions and distributions91D95CD7
2.5 Convolution and mollifiersE5DAA0D27299
2.6 Weak convergence of measuresA1AF2491CD1A
2.7 Nets and compactness796552E62FD2
2.8 Densities and differentiation of integrals9563E8B823D2
2.9 Fourier analysis and incidence of complex lines99FBE9B23B3C

Chapter 3. Harmonic and subharmonic functions611E147E5D10

3.1 Harmonic functions and the Dirichlet problem952EDF2CE146
3.2 Kelvin transforms and half-space potentials9728BD930155
3.3 Classical harmonic analysis4061AEE18413
3.4 Subharmonic functions0BBC054FD2E1
3.5 Green functions and potentials16EB8324A3E2

Chapter 4. Energy, capacity, and fine topology9FF63F7CB15D

4.1 Potentials, energy and capacity765E6C8792CB
4.2 Fine topology and balayage8618E9B4AA3D
4.3 Polar sets, capacity and sweepingAEB997E884B4
4.4 Perron theory and fine boundary limits5CFAC22DC258
4.5 Green energy and Martin boundaries8D29421CAE4C

Chapter 5. Plurisubharmonic functions and positive currents870EA66136BC

5.1 Complex differential forms and positive currents4DEEEF894245
5.2 Complex manifolds and differential formsD8E2D1A98ACF
5.3 Currents and positivityACB622806098
5.4 Local potentials for closed (1,1)-currents618FE2108D26
5.5 Holomorphic zeros and the Poincaré–Lelong formula0C34F7796300
5.6 Maps of currents and local mass9F1C9C4A649E
5.7 Plurisubharmonic functions7B39B08A9568
5.8 The line definition and upper semicontinuity55393AEE99C8
5.9 Positive Hessians and holomorphic maps484A05EF6DF1
5.10 Limits, envelopes and local integrability5C7282E51B13
5.11 Extension across closed exceptional setsE197EAFECEC0
5.12 Kiselman's minimum principle53A48113C242
5.13 The definition of plurisubharmonic functions92A4FA45DFE1
5.14 Properties of plurisubharmonic functions6C47792FE6D9
5.15 Plurifine topologyDFFF533F1AE8
5.16 Lelong numbers and multiplier ideal sheavesEB678D619AD9
5.17 Quasi-plurisubharmonic functions4DF694F99750
5.18 Analytic singularities26AEEBDF865B
5.19 The space of currentsEB85809E6CA8
5.20 Plurisubharmonic metrics on line bundlesA59F8B8F06A8
5.21 Plurisubharmonic functions and singularitiesEDB5A2485B58
5.22 Plurisubharmonic potentials17A37A0D3690
5.23 Changes of background012278DBB6E8
5.24 Maxima and the maximum principleAA6F3BC0AD9F
5.25 Normalized compactness0B216F0B911E
5.26 Uniform exponential integrability5A19CE5C3CCE
5.27 Local products and capacity5E507B6993DC
5.28 Products with smooth backgrounds5E2B332B89B4
5.29 Hermitian capacityDD310AD8B258
5.30 Comparing local regularizationsDB8E63271D73
5.31 Gluing with a small curvature error78243032B1A1
5.32 Regularization in a fixed Hermitian background26C061D9E9B2
5.33 Singularity type and multiplier ideals9A10411F1BCD
5.34 Analytic types and restriction0D77FC17B23B
5.35 The local Bergman estimates51F374296336
5.36 The global curvature bound3BCA55154463
5.37 Multiplier ideals and logarithmic poles5BB7B3EA169D
5.38 Lelong numbers and divisorial estimates2C2417A75DF4
5.39 Potential regularity and metric distanceDE3129821F10
5.40 Obstacle envelopes8EA2EE30DE99
5.41 The minimum principle392B79314DF8
5.42 Chern-connection regularization001730C9ED64
5.43 Pullback and descent88AEFA5005B9
5.44 Integration against non-pluripolar measures2111608E9FA1
5.45 Curvature of line bundles355A31F789F6
5.46 Polar curvatureAFA07BFD0E7B
5.47 Pluripolar sets and the plurifine topologyF5A3147592B6

Chapter 6. Lelong numbers, multiplier ideals, and regularization9B85831FAA0C

6.1 Weighted L2 estimates and holomorphic extension89143AD4638F
6.2 Hilbert spaces and closed operator complexes3F2EA9D1CB5E
6.3 Pseudoconvexity and boundary distance86B639827902
6.4 Interior density and the weighted estimate4E04198982E6
6.5 Interpolation and extension across a hyperplane6FAB73FA6CE4
6.6 Lelong numbers and multiplier ideals8494F0D4F79D
6.7 Logarithmic growth and the Jensen formula4939444F8FDD
6.8 Coherent ideals from weighted integrabilityC6A4B68C3F0B
6.9 Analytic Lelong level sets and generic valuesDB8FD0974B86
6.10 Restriction, products and integral closure3E60ECFFA1E9
6.11 Strong openness by extension from moving slicesF441BF47EB53
6.12 Birational change of variables and logarithmic thresholdsBC64CE221556
6.13 Analytic singularities and Demailly approximation1A5FE90C1245
6.14 Smooth backgrounds and analytic singularitiesA4223F8F8B02
6.15 Local Bergman kernels and ideal generators9C2A6446C90A
6.16 Overlap interpolation and quantitative patching0B2C9E3CF86E
6.17 Smooth cutoff sums and decreasing approximationB4D51CAC5833
6.18 Comparison of analytic singularities625C998FCF3C
6.19 Bounded growth ideals3951ADFEE2AB

Chapter 7. Local Monge–Ampère theory and capacityAB4C5F4E80F4

7.1 Bedford–Taylor products and local capacity2F5912FF9FEA
7.2 Bounded potentials and recursive products4272F622A446
7.3 Decreasing continuity and symmetry2CE0DCA46BB5
7.4 Weighted estimates and Monge–Ampère capacityCD19E1C1FD36
7.5 Quasi-continuity and convergence in capacity887374BF3465
7.6 Increasing limits and exceptional envelopesE5550B44EC7B
7.7 The homogeneous Dirichlet problem and balayage22EC1FF0BE9D
7.8 Density lower bounds and mixed products2044B813A798
7.9 The ball Dirichlet problem with continuous density0897D387268D
7.10 Bounded measurable densitiesD4D4A913D86D
7.11 Local energy moments867F8B92120A
7.12 Mixed products for a common measure07DF7DC201F0
7.13 Bounded complex Hessians and contact setsFB1768F3514F
7.14 Gradients against positive currents166A7FDE3C64

Chapter 8. Complex Hessian equationsF0BC19D39AE4

8.1 Complex Hessian equationsCFD38285654D
8.2 The admissible coneF677D35E0BD7
8.3 Liouville and gradient estimates1B647CA2D005
8.4 A trace estimate with a prescribed potential54309E0621C2
8.5 Bounded complex Hessians and elliptic extensionsEA00781761AE
8.6 Proper equations and admissible approximationA493740DE457
8.7 Continuous products, envelopes and domination5B2332FC78E2
8.8 Continuous equations and regularityD5976AE10288
8.9 Bounded potentials and recursive Hessian currents376A2B30178D
8.10 Sobolev capacity and two Hessian factorsFB2B0B645AB5
8.11 Local capacities and decreasing productsBA5052EF5C4F
8.12 Locality and maxima of bounded potentials927D22F5110F
8.13 Hessian mass and global comparisonB908310EE8A2

Chapter 9. Complex spaces and modifications7C326140E164

9.1 Complex spaces and modificationsB64C7FEAE2E7
9.2 Division and finite analytic modulesD4E6B7455291
9.3 Analytic sets and their local branchesA49B7CFC7FBF
9.4 Reduced spaces and normalizationC16A2F5D9879
9.5 Analytic curves and finite maps2BDD13613B99
9.6 Blowups and resolution25A311AD092F
9.7 Proper images and relative principalization05BF24D5DFA6
9.8 Connected fibers and resolution modelsF0CABED1A01F
9.9 Plurisubharmonic functions on reduced spaces75F10F3C1577
9.10 Pluripotential theory on unibranch spaces5131A8B4E30A
9.11 Potentials and equations on unibranch spaces77EFAFB55325

Chapter 10. Cohomology, positivity, and geometric lociF5E2239DEBA0

10.1 Global potentials and positive cohomology classesCFDF01A8B5A7
10.2 The trace equation and global potentials308B81D53CDF
10.3 Normalized potentials and minimal singularitiesF0B52F4D634F
10.4 Positivity cones and divisorial decomposition8E4902BB309B
10.5 Minimal multiplicities and positivity loci272951B4998D
10.6 Curvature and metrics defined by sections01A60CA78CF8
10.7 Compact interpolation and global Bergman kernels9BE85E662C13
10.8 Extension from a compact submanifold9264FE392E91
10.9 Global poles on compact complex manifoldsAC5D271E1A27
10.10 Bott–Chern classes and singular loci26958A01D807
10.11 Closed classes with Hermitian lower bounds827D49511DDA
10.12 Minimal multiplicities and the non-nef locus1FFB44AD196A
10.13 The non-Kähler locusB0A0B0442070
10.14 Null loci and numerical restricted volumes9CCCA75301B4
10.15 Restricted volumes and Hermitian perturbations66B7922BA301
10.16 Finite restricted masses of closed classesA8A4EA7F273E
10.17 Divisorial traces with bounded remainderBB144FEBF316
10.18 Divisorial components at the threshold89CEBB4B3B57
10.19 Currents on the elliptic threefoldB9786385D8CD
10.20 Smooth equations on the ample locusF93BA59ECB83
10.21 Density zeros and metric degenerationAE84FAD03138
10.22 Radial densities and metric completeness623ED03FC0EE
10.23 Equations on products with a curveFE10733FC7A7
10.24 An incomplete metric in a big classE61E86F27D3F
10.25 Normal length near a divisor4F870C264678
10.26 Rigid boundary classes on a torus5A68768CC1C3
10.27 Nonrigid classes on a quotient resolution96EA3D3C069F
10.28 Semipositive metrics in a four-point blowup family058F9CA104B3
10.29 Oeljeklaus–Toma manifolds9F59E018A291
10.30 Classes with a nonclosed backgroundFB4254C93740
10.31 Big backgrounds under bounded massC2AE04961A4E

Chapter 11. Hermitian geometry, torsion, and Gauduchon duality298536BFFEA2

11.1 Torsion and the variation of mass7B453010B5B8
11.2 Monge–Ampère energy and torsion1FC29EAFAA97
11.3 Gauduchon metrics and linear mass1009E65ECC4C
11.4 Conformal Gauduchon metrics4ECC3E68F7D5
11.5 Conservation of the trace massA21D56C40154
11.6 The Gauduchon criterion for positivity6029C37CE10F
11.7 Compactness and duality of Gauduchon currentsA532E9A2E94A
11.8 Transverse concentration of Gauduchon tests959649DAC54D
11.9 Convex norms and Gauduchon degrees93399AABE3EC
11.10 Homogeneous convex regularization879A1C19426E
11.11 Strict positivity from the tautological metric733548AD7779
11.12 Polar norms of semipositive Finsler metricsC40892E1279D
11.13 Ample comparison quotients on Hirzebruch surfaces9C2F19628D6F
11.14 Stable extensions approaching the split comparison bundleD9D859664CFB
11.15 Deforming to stable ample bundlesE22565883FFD
11.16 A fixed Stein hypersurface for all Finsler metricsFE1ACFDCD4DA
11.17 Concave neighborhoods and dual norms4276F3B6339D
11.18 Curvature and projective complement exhaustionsF56029D8C19A
11.19 Negative bundle metrics and logarithmic weightsEF53CEC272DE
11.20 External tensor products and complement convexity391E9AF09F50
11.21 Homogeneous plurisubharmonic functions and Hopf complements2ADE48A8B892
11.22 Pluriharmonic currentsB57478F1D4E4
11.23 The adjoint measure of the linearizationC01896004229
11.24 Fredholm theory for a continuous Hermitian formDB480BD29A98
11.25 Limits of adjoint measures8B86B2B0A308
11.26 Conformal changes and directional curvature positivityA4E01A8B6F30
11.27 Ricci-flat Kähler surfacesFFC070E9C8C2
11.28 Holomorphic sectional curvatureAF4D6581275D
11.29 Projective first jets and positive bundle metricsA1CB99CAE47B
11.30 Ramified section tests and a positive root metricEF54BD838F8D
11.31 Gauduchon traces and the topology of potentials15943A2C3613
11.32 Normalization and weak adjoint measures7091FEDB43F0
11.33 The scalar functional52D96CD9BFA7
11.34 Supporting probability measuresEE2EC5B3CDE0
11.35 A convex functional on probability measuresD8DD45551DB2
11.36 Bounded measurable densities and stability0E821D2FEC9D
11.37 Entropy and the closed case694B6AE5D5E5
11.38 Entropy bounds531A2D2A66CF
11.39 Changing the prescribed singularities44DF399743E5
11.40 Varying positive backgroundsABAC4E4BC446
11.41 Divisorial types and moving sections2D3AC831EDA6
11.42 The mass determined by the functionalF459A353BA9B
11.43 Convex-body criteria for varying references7D0D0E9AC5C3
11.44 Selection by a vanishing exponential parameterDB96849B14F8
11.45 Selection for logarithmic models on productsA167FA614566
11.46 Residual regularity in radial singularity typesDF55B983AF23
11.47 Envelopes for singular radial obstaclesAEE10281DB3D

Chapter 12. Gauduchon variational volumeA93AA52F4C7A

12.1 A Gauduchon variational volume881C26425D7A
12.2 The quotient and the smooth equation43BF29E33E59
12.3 The equality case of concavity and the first variation484879715C58
12.4 Second variation on background classes8A687EAB6B68
12.5 Recovering a positive class from its Gauduchon derivative9141861B4F50
12.6 The Hessian metric and its completion466CEDF9AEBA
12.7 A compact dual problem over Gauduchon currents54ADA5D399DA
12.8 Supporting probabilities represented by maximizing currents7C2BB0FDDDF5
12.9 Integrability of Gauduchon determinant measuresD02094988A03
12.10 Integrable densities in the compact Gauduchon problem5CB8CFC32A19
12.11 Nef limits and nonattainmentEA449D56F8F7
12.12 Subtraction with a closed nef core75F31FAA4616
12.13 Subtraction on warped productsEA9388E29ABC
12.14 Positive volume without bignessE4AB7B03C20D
12.15 Varying the probability measure8B161DDAE77F
12.16 Curvature conditions for mass extremaA57EC3129CC8
12.17 Curvature pairs and positive lower massC18EABD7D630
12.18 Geometric bounds and determinant concentrationAA652CC345D8
12.19 Vanishing lower mass108F40B2DFAA
12.20 Orders of degeneration at the nef boundary3567ADAA7365
12.21 Elliptic surface volumes and order spectraE4B29689FB79
12.22 Comparison under an arbitrary modification9BED3D691F82
12.23 Strict changes under one blowupD0D47B7389D7
12.24 Positive-current subtraction and divisorial residuals57C0ECEB4F4C
12.25 Integer orders in fixed projective conesE6D8A97F4D2C
12.26 A maximum-rank comparison criterion493311C8FB2F
12.27 Flat anticanonical curves0E9176045572
12.28 Flat divisors and Hartogs extension25D1457FC429
12.29 Punctured line bundles and elliptic quotients76F771FE4DA3
12.30 Cotangent torsors on split elliptic ruled surfacesE4B698D2AEE3
12.31 Symmetric tensors on split elliptic ruled surfaces7CF6C47CAA92
12.32 Section algebras of cotangent extensions72E247F3A7CA
12.33 Cotangent extensions with zero ruling componentC9CE007F34A7
12.34 Current tests for smooth positivity509A5021C77D
12.35 Divisorial constraints and residual volume269CE892EA5B
12.36 A divisorial threshold on the Hopf threefold7F944D8C8D92

Chapter 13. Non-pluripolar measures and massAAF7D28E18FB

13.1 Non-pluripolar productsE478B9E17C75
13.2 Truncation and plurifine localityA56454EDE5B3
13.3 Closedness and cutoff gradients4D61EAFD1D21
13.4 Bounded factors and the first-degree productF483C973DB98
13.5 Global finiteness and bounded cohomological mass48A11CF18369
13.6 Fiber integration and modificationsFBE95DA26374
13.7 Capacity convergence and loss of mass52BF527413C6
13.8 Mass comparison and projective fibersC76D4F3419F8
13.9 Maximal mass and comparisonCCB85E469493
13.10 Bedford–Taylor theory7CD616A8B803
13.11 The non-pluripolar products77A0C8665B8A
13.12 Quasi-continuous functionsAD5CC24EA726
13.13 Properties of non-pluripolar products01C01D21DDD2
13.14 Non-pluripolar Monge–Ampère measuresB724B74AE68C
13.15 Weighted Monge–Ampère measuresA6A92DB9F7DA
13.16 Volumes under bounded massEEFEDC3AE6FE
13.17 Comparison of singularity volumes32986EE97902
13.18 Volume deficits and relative full massE8D1B2CE6F8F
13.19 Domination and ordinary envelopes832E0568D7C3
13.20 Strict barriers and background variation904042ECF361
13.21 Monotone limitsA8EAC258D61B
13.22 Cauchy convergence of model potentialsF1D6B77D3DEE
13.23 Rooftops and capacity convergence1D6292952FE6
13.24 Volumes of multiplier-ideal envelopes146F3DD22A85
13.25 Model comparison under background changesB2557A0A9699
13.26 Two-sided background perturbationsE6BBFE91C762
13.27 A complete metric on positive-volume models7EAA1D7446C4
13.28 Model potentials on curvesE6AC80354EB9
13.29 Background changes on curves3A638A8288E0
13.30 A complete space over varying curve backgroundsF36B844DE285

Chapter 14. Monge–Ampère equations and stabilityABAD0B75D26A

14.1 Smooth Monge–Ampère equations92B1F482D72A
14.2 Scalar bounds and uniqueness5E342E12EF34
14.3 The potential bound from weighted integrationD57A1C84047D
14.4 The linearized equation and smooth dependence7BDF4C42EB78
14.5 Second derivatives and ellipticityCBFCDA7183ED
14.6 The continuity methodF1D5D01E2624
14.7 The smooth exponential equationA4D09B787D84
14.8 Variation of the normalization scalar9541740AAFDC
14.9 Normalization on the Hopf threefold44E03525BBAF
14.10 Prescribing a Gauduchon volume form6950E7B1FBCB
14.11 Bounds for the Gauduchon potentialF9FF7B5E741A
14.12 The adjoint equation for Gauduchon volumeF6A1B32989A1
14.13 The matrix structure of the Gauduchon equation53E844FE515C
14.14 The largest-eigenvalue estimate148E6041EC3F
14.15 A Liouville theorem for the limiting coneD4DE203BE3BF
14.16 The gradient bound by rescaling40669ABC11F8
14.17 Existence for the Gauduchon ansatz6904C64D5831
14.18 Normalization for the Gauduchon equation9C1043361EBF
14.19 Continuous solutions and normalization080A6052D542
14.20 Uniqueness for degenerate equations6B1310DDF7B5
14.21 Extrema and density sublevels6267D9D97C43
14.22 Polarized cofactors and propagation9769545E981A
14.23 Integral rigidity in dimensions two and three4DE5082C1B2B
14.24 Bounded uniqueness and connectednessE0DB623401C5
14.25 Comparison and invariant mass48CE016DFF65
14.26 Smooth nonuniqueness for a degenerate densityD85397FA2C2A
14.27 Nonuniqueness with a zero set of empty interior5278ECB27C50
14.28 Quadratic density zeros9ABE80D68F2B
14.29 A real analytic densityC3B76FE21E71

Chapter 15. Monge–Ampère equations with prescribed singularitiesEAB08B331BC2

15.1 Equations with prescribed singularitiesF9AE3BF05078
15.2 Domination with a smaller background2ACF52860663
15.3 Bounded equations in a semipositive big background9F0629AA9014
15.4 A quantitative stability estimateB4FB50E0C9DE
15.5 Hölder continuity from bounded stabilityBDF9BACE965B
15.6 Local continuity in a semipositive big backgroundFF4EC5CCEA0B
15.7 Homogeneous replacement on a coordinate ball35C79FB822EF
15.8 Contact support in a big backgroundACC753805E21
15.9 Compactness with a common lower barrierD6040BDF0454
15.10 A bounded subsolution theorem898B7B54B3D0
15.11 Adding weighted Monge–Ampère measures7BAAE1AD9F47
15.12 Equations in a prescribed ordinary typeC6737BA51F0E
15.13 Comparison above a strict singular barrier1FCAFCAE9C0E
15.14 Subsolutions and the Gauduchon trace8C0AAADFFCFC
15.15 Stability above a strict barrierA7C7BC261679
15.16 Minimal singularities in an arbitrary big background5961B4E1812C
15.17 Local Hölder continuity in a big background1A5D83E43B0A
15.18 Interior smoothness on the regular locus899B82DE5E84
15.19 Degenerating semipositive backgrounds28A495F29AAD
15.20 Symmetry and the selected projective limit457A6A4C41F4
15.21 Local density and boundary controlD0D15F32906B
15.22 Equations with resolved logarithmic poles3A4DA254E4F4
15.23 Minimal singularities on blowups3F1CADE9F6C1
15.24 Representing measures in an ordinary type2BB76C1E3909
15.25 The homogeneous equation with a Hölder reference679A3E78F3EA
15.26 Singular measures on shrinking spheres4BA6AFA61CAA
15.27 Lower mass and solvability for all measures93CEF832AEA2
15.28 Subsolutions for an individual density72CDE5ADD348
15.29 Gauduchon tests for integrable densities7B44C03D318B
15.30 Exact equations on products with zero lower massFC44870E2A2C
15.31 Singular measures on products with a curveE01ACE366291
15.32 Stability of the subsolution threshold06284CD8A9D4
15.33 Power capacity bounds and threshold equations119B0BE69A7D
15.34 Limits of exponential equationsB63DDE7640A4
15.35 Exponential equations for an individual densityC3635E28D6B1
15.36 Radial selection for integrable densitiesC10FB3AB7407
15.37 Relative equations under positive lower mass31A655BFE398

Chapter 16. Singularity types, envelopes, and models5FC17142DBF9

16.1 The envelope operators2AC9E2799656
16.2 P-envelopesA6FA63C034E6
16.3 Rooftop operator and the definition of the $P$-envelope1BFD41225C11
16.4 Properties of the $P$-envelope666167293D79
16.5 Relative full mass classesB22CE32B08DB
16.6 Multiplier-ideal envelopes3FB831210DD1
16.7 Comparison of singularitiesDE52193AE570
16.8 The $P$ and $\mathcal{I}$-preordersEC95C2958023
16.9 The $d_ S$-pseudometric45BED73AEFE3
16.10 Envelopes and model potentialsCC5E34310EEC
16.11 Obstacles and rooftopsFBD81D436A6A
16.12 Measures on contact sets87B472751372
16.13 Concentration on the contact set954F538078ED
16.14 Obstacles with bounded metric Laplacian74F4AD99CB8E
16.15 Penalized equations and metric-Laplacian envelopesF9CE743055E9
16.16 Real Hessian bounds for Kähler envelopes20C85925F87F
16.17 Smoothing and its joint complex HessianB73B45463F24
16.18 A minimum with a varying upper radius8DF7590E8FE8
16.19 Big-class envelopes on the ample locus422B4DDB7F36
16.20 Contact with an arbitrary singular potential99AF407A4E55
16.21 Singularity envelopes88E8C70208D8
16.22 Extrapolation and model singularities472B5CD7929C
16.23 Rooftops and mass inequalities4CC29395A55C
16.24 Divisorial constraints under envelopesA7364A53065E
16.25 Singularity constraints and relative capacity2B1B1CB179EE
16.26 Quantitative rooftop extrapolation5928CB7C3BCE
16.27 Comparison of relative capacitiesDE4415660D60
16.28 Envelopes and volumes of singularities168D3DF32068
16.29 Envelope systems over Hermitian perturbations4AD4DDD929EE

Chapter 17. Energy, geodesics, rays, and test curves8ACCDAB4280C

17.1 Relative energy and Perron segmentsBDB8E5100372
17.2 Integration by parts for bounded differencesF694A6981C1D
17.3 Relative Monge–Ampère energyEC60D9ED3C42
17.4 Continuity and compactness3B8286222A1B
17.5 Variational Monge–Ampère equations16614E7E6F9C
17.6 Singularity envelopes at arbitrary mass178F9F7684F6
17.7 Subgeodesics and Perron segments4C4B950F1CFF
17.8 Energy along weak geodesics0753F06C3AFA
17.9 Extremal slopes and long Perron segments66FE6F0ACABE
17.10 Geodesic rays in the space of potentials1E44B710CD7B
17.11 Test curvesBA6AA7598BE3
17.12 The notion of test curves908139B245F5
17.13 Ross–Witt Nyström correspondenceC9D15D724069
17.14 -model test curvesCAE331B64333
17.15 Operations on test curves9D751AA26579
17.16 Perron interpolation and the geodesic equationE4ED60C8BCA5
17.17 Test curves and Legendre dualityD5DBDCE92D6A

Chapter 18. Multiplier-ideal models and partial equilibriumE0D5368D9D4A

18.1 I-good singularitiesA058A93BF381
18.2 Multiplier-ideal envelopes and I-goodness530E72454328
18.3 The Kähler characterization649A8A26E78B
18.4 Ideal projection3458DC26AA54
18.5 Changes of background and envelope massFD3DFA6C79CF
18.6 geometry of ideal classes3D693DBCCBE2
18.7 Limits of analytic envelopesE69A0F80536C
18.8 A topology on ordinary singularity types8E117060E468
18.9 Analytic closureE3C1856717ED
18.10 Separation and mass85FB0412C472
18.11 Transport with an obstacle2C83B2C35668
18.12 All smooth obstaclesB61E129D450F
18.13 Countable poles and all obstaclesA941DC64EED0
18.14 Relative divisors and fiber obstaclesF77ABCE68FED
18.15 Divisorial products and zero volumeFCC95AC9CD7B
18.16 Several curve factorsCCB2410A352E
18.17 Varying the curve coefficientsE1C8539A70B7
18.18 Arbitrary curve backgrounds16EA76D7DAAB
18.19 Equality below all obstacles on separated products627A32EBF892
18.20 Auxiliary compact complex factors42B1A5F53675
18.21 A polar metric in a background with unbounded mass49135DC5A99F
18.22 Models over a curve00A545D724DB
18.23 Finite curve factors9BCD2B4E97EF
18.24 Models pulled back by a finite curve mapEB49D847F199
18.25 Hopf surface fibers and unbounded ambient massB094CC4C0076
18.26 Complete model topologies987BD480177F
18.27 Small curvature and strict ordinary types0A2CF48796FA
18.28 Partial Bergman kernels065B04510A8A
18.29 Partial kernels and quotient equilibriumB52A879692D6
18.30 Selected spaces and partial Bergman kernelsF62F806EF43E
18.31 A local Bernstein–Markov estimate71CAA1E8F43F
18.32 Partial envelopes on a weighted compact set848269EDF931
18.33 An upper bound for partial Fubini–Study limits2502C12D48F4
18.34 The determinant functional3AC0CF30AE00
18.35 Partial kernels under a modificationD537C70B64A0
18.36 Kernels on a fibration8EDC1869ED38
18.37 Isolated logarithmic poles on a fibration79DB60788E3F
18.38 A point pole on the Hopf manifoldCFB70C5F514C
18.39 Singularities along a section over a divisorDFED5BDE8678
18.40 Horizontal poles over projective space6109F3CDB146
18.41 Degenerate curvature and growing vanishing orders99460DD0DBB7
18.42 Localization on curvesB3DCF0B463CE
18.43 A logarithmic kernel scale in two dimensions9C0BFE5CB0FF
18.44 Anisotropic point jets and isolated poles on fibrations44BF9B7D0141
18.45 Newton selection and moment-shell limits5CEF27CB9AAA
18.46 Rounding in multiplier-ideal kernel families73EEA7DBAB83
18.47 Three monomial bands from a multiplier-ideal selection435C250083A1

Chapter 19. Sections, graded series, and Okounkov bodiesA24B3AAE0C3C

19.1 The theory of Okounkov bodies2DF8DA44EB89
19.2 Almost semigroups1ED20E6196A2
19.3 Flags and valuationsE9A341A325BE
19.4 Algebraic partial Okounkov bodiesC9B9B0985C6B
19.5 Transcendental partial Okounkov bodiesA2D41AECAD65
19.6 Okounkov test curvesBC31851ECB21
19.7 Almost semigroups00B44728CC57
19.8 Holomorphic sections and Hermitian mass725C2F97B643
19.9 Flags, convex bodies and section growth926A00196D5E

Chapter 20. B-divisors and restriction93ECB0A22161

20.1 The theory of b-divisors1EAF89CE07E1
20.2 The trace operator007D02149D2D
20.3 Restriction and intrinsic trace dataE6AE4A881F9F
20.4 Divisorial currents on compact modificationsD53B61AD71E9

Chapter 21. Toric and convex geometryFB639626E34C

21.1 Convex analysis and toric potentials4C57CCF28620
21.2 Closed convex functions and supporting slopes5430067C9C99
21.3 Legendre duality and convex envelopesEC0F5475F1C8
21.4 Slope bodies and bounded growth8CD47210DEE8
21.5 The real Monge–Ampère measure07CCE1F902ED
21.6 Compact convex envelopes and full-mass limits2F45C4BAC276
21.7 Lattice points and volume2479DAC58B22
21.8 Smooth lattice polytopes and projective chartsF916BA03200F
21.9 Fans, divisors and character sectionsFF296752801A
21.10 The Guillemin reference metric256A3051D9FC
21.11 Convex functions and convex bodies9A65EFDDFA3F
21.12 Toric pluripotential theory on ample line bundles6F5A4A494129
21.13 Toric pluripotential theory on big line bundlesF1FA15E12648
21.14 Hopf fibrations and toric potentials23660BEC4C1F

Chapter 22. Non-Archimedean pluripotential theory126156CA1DEA

22.1 Non-Archimedean pluripotential theory1E9C5D0261FD

Chapter 23. Hopf and locally conformally Kähler geometryBF36ACCFA224

23.1 Unbounded mass on Hopf manifolds142249962360
23.2 Locally conformally Kähler geometry9B4394B392ED

Chapter 24. Problems in pluripotential theoryF03E578EF455

24.1 Problems in Hermitian pluripotential theory9226B45701D5
24.2 Threshold equations and singular limitsA1CD1701B975
24.3 Positive Gauduchon volume and bigness6CDBB1FBABB2
24.4 Closed positivity and geometric equations8871793F78BB
24.5 Closed and twisted classesB3F20D9F0DB0
24.6 Degeneration orders and finite-distance boundaries7B777ACFF4E8
24.7 Weak Gauduchon adjointsC528B286A8D7
24.8 Topologies on singularity types103C284C8243
24.9 Trace realization and recovery1B042D04CEDB
24.10 Sections, kernels and the dimension of growth86B65C86A5FA
24.11 Equations on singular spacesC6BAF3541DDF

Chapter 25. Historical and bibliographical notes3168511224C4

25.1 Historical and bibliographical notes65E16F3944C7
25.2 Historical notes4D6830B53C70
25.3 Plurisubharmonic functions and regularization9D79D5D188C6
25.4 Mass and energyBB36F353AA0C
25.5 Gauduchon metrics and positivity3C68E80772A5
25.6 Bounded products and extended measures9E2E80C382FD
25.7 Envelopes and comparisonCA53357795CC
25.8 Smooth and continuous equationsE1BC130DDD5C
25.9 Uniqueness and selectionAFDCC356D816
25.10 Complex Hessian equations67A66AB9757E
25.11 Volumes under mass boundsD116D93B0EBE
25.12 Equations with prescribed singularitiesEFAA097B03EC
25.13 Normalization and adjoint measures7B9538DE7653
25.14 Perron geometry on Hopf manifolds94E3F780653C
25.15 Singularity classes and traces81F92F228A7E
25.16 Section growth and partial kernelsCAFE5EFFA7C8
25.17 Gauduchon variational volume3747CBC0FB2D
25.18 Closed classes and singular lociC873148DF75D
25.19 Closed classes and metric completeness6DFCF19530CA
25.20 Locally conformally Kähler geometry2C3E73AAD887
25.21 Regularity and singular spaces2200D43D6A26
25.22 Geometric problemsBCAE26692B2F
25.23 CommentsF8F49090AB94

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@misc{pome-home,
  author = {{Pome contributors}},
  title = {Pome},
  howpublished = {Pome},
  url = {https://mingchenxia.github.io/Pome/}
}

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