Chapter 10

Cohomology, positivity, and geometric lociF5E2239DEBA0

Global potentials, positive classes, Bott–Chern geometry, and singular loci.

Sections and subsections

1. 10.1 Global potentials and positive cohomology classesCFDF01A8B5A7
2. 10.2 The trace equation and global potentials308B81D53CDF
3. 10.3 Normalized potentials and minimal singularitiesF0B52F4D634F
4. 10.4 Positivity cones and divisorial decomposition8E4902BB309B
5. 10.5 Minimal multiplicities and positivity loci272951B4998D
6. 10.6 Curvature and metrics defined by sections01A60CA78CF8
7. 10.7 Compact interpolation and global Bergman kernels9BE85E662C13
8. 10.8 Extension from a compact submanifold9264FE392E91
   1. 10.8.23 Extending strictly positive potentials963CD0DB428C
9. 10.9 Global poles on compact complex manifoldsAC5D271E1A27
10. 10.10 Bott–Chern classes and singular loci26958A01D807
11. 10.11 Closed classes with Hermitian lower bounds827D49511DDA
12. 10.12 Minimal multiplicities and the non-nef locus1FFB44AD196A
13. 10.13 The non-Kähler locusB0A0B0442070
14. 10.14 Null loci and numerical restricted volumes9CCCA75301B4
15. 10.15 Restricted volumes and Hermitian perturbations66B7922BA301
16. 10.16 Finite restricted masses of closed classesA8A4EA7F273E
17. 10.17 Divisorial traces with bounded remainderBB144FEBF316
18. 10.18 Divisorial components at the threshold89CEBB4B3B57
19. 10.19 Currents on the elliptic threefoldB9786385D8CD
    1. 10.19.3 Potentials and envelopes from the base7CFF33409C17
    2. 10.19.5 Sections selected by multiplier idealsE99505EBA4B4
    3. 10.19.7 The boundary volume and section growth714E787B0503
    4. 10.19.10 Limits of the minimizing Gauduchon forms7128CD1C74CB
20. 10.20 Smooth equations on the ample locusF93BA59ECB83
21. 10.21 Density zeros and metric degenerationAE84FAD03138
    1. 10.21.5 Determinant and normal distanceC03017CE71E3
    2. 10.21.8 Smoothness of exceptional residuals1B7310DAABFD
22. 10.22 Radial densities and metric completeness623ED03FC0EE
23. 10.23 Equations on products with a curveFE10733FC7A7
24. 10.24 An incomplete metric in a big classE61E86F27D3F
    1. 10.24.6 A nef class with an incomplete null end903A353086FC
    2. 10.24.13 An incomplete metric with compatible flow data76505E13E4B8
25. 10.25 Normal length near a divisor4F870C264678
    1. 10.25.7 The critical exponent on a compact torusD95BCCFE2A18
26. 10.26 Rigid boundary classes on a torus5A68768CC1C3
27. 10.27 Nonrigid classes on a quotient resolution96EA3D3C069F
28. 10.28 Semipositive metrics in a four-point blowup family058F9CA104B3
    1. 10.28.5 The image of metric restrictionBBAE9B00E672
29. 10.29 Oeljeklaus–Toma manifolds9F59E018A291
    1. 10.29.1 The constructionCA83ED725CCA
    2. 10.29.2 Potentials of the transverse form992E9A24F805
    3. 10.29.8 Monge–Ampère masses on threefoldsDF61FAE7D603
    4. 10.29.13 Hermitian metrics whose $\mathrm{dd}^{\mathrm{c}}$ has a signD5CAAE8D5B60
30. 10.30 Classes with a nonclosed backgroundFB4254C93740
    1. 10.30.1 Affine classes with prescribed derivative89D86926636A
    2. 10.30.3 Residual trace classesC43F5C12FA6F
    3. 10.30.6 Nef realizations and residual-current limitsAFB10A9AB20B
    4. 10.30.9 Divisorial classes and infinite mass47AA4DD512F8
31. 10.31 Big backgrounds under bounded massC2AE04961A4E
    1. 10.31.2 Equations for finite measures71BC8ED98CA7
    2. 10.31.4 Convergence under a fixed measureD176FBCC507C
    3. 10.31.7 Relative moments985DB0A9A096
    4. 10.31.13 Higher moments in the minimal singularity type811851E56701
    5. 10.31.18 General measures in the minimal class0AD35E504E60
    6. 10.31.21 Exponential and normalized equations6720AA8AAF70
    7. 10.31.24 Relative projection and supersolutions4FA2BA45E658
    8. 10.31.29 Varying model references4A341D55C924
    9. 10.31.33 Weighted measure additionDA040FEBC40C
    10. 10.31.37 Ordinary types and bounded carriers11CC2B98E362
    11. 10.31.43 General measures with a model reference10C7F976A14C
    12. 10.31.46 Stability under changes of reference4D69742DF215
    13. 10.31.48 Arbitrary weighted sums9E6F276DB6E3
    14. 10.31.52 Relative boundedness for $L^ p$ data2CD3B93A6226