Chapter 16

Singularity types, envelopes, and models5FC17142DBF9

Singularity order, rooftop and model envelopes, and Hermitian perturbations.

Sections and subsections

1. 16.1 The envelope operators2AC9E2799656
2. 16.2 P-envelopesA6FA63C034E6
3. 16.3 Rooftop operator and the definition of the $P$-envelope1BFD41225C11
4. 16.4 Properties of the $P$-envelope666167293D79
5. 16.5 Relative full mass classesB22CE32B08DB
6. 16.6 Multiplier-ideal envelopes3FB831210DD1
   1. 16.6.1 $\mathcal{I}$-equivalence6C0625A38157
   2. 16.6.6 The definition of the $\mathcal{I}$-envelope39E4D656BD09
   3. 16.6.26 Properties of the $\mathcal{I}$-envelope4FA5F6B29982
7. 16.7 Comparison of singularitiesDE52193AE570
8. 16.8 The $P$ and $\mathcal{I}$-preordersEC95C2958023
   1. 16.8.1 The definitions of the preordersF7493F03C4C2
   2. 16.8.21 Properties of the preordersF4304BE7EF91
9. 16.9 The $d_ S$-pseudometric45BED73AEFE3
   1. 16.9.1 The definition of the $d_ S$-pseudometricBB740CB4BE99
   2. 16.9.26 Convergence theorems0BF3C2E4260B
   3. 16.9.54 Continuity of invariantsF6973807BD19
10. 16.10 Envelopes and model potentialsCC5E34310EEC
11. 16.11 Obstacles and rooftopsFBD81D436A6A
12. 16.12 Measures on contact sets87B472751372
13. 16.13 Concentration on the contact set954F538078ED
14. 16.14 Obstacles with bounded metric Laplacian74F4AD99CB8E
15. 16.15 Penalized equations and metric-Laplacian envelopesF9CE743055E9
16. 16.16 Real Hessian bounds for Kähler envelopes20C85925F87F
17. 16.17 Smoothing and its joint complex HessianB73B45463F24
18. 16.18 A minimum with a varying upper radius8DF7590E8FE8
19. 16.19 Big-class envelopes on the ample locus422B4DDB7F36
20. 16.20 Contact with an arbitrary singular potential99AF407A4E55
21. 16.21 Singularity envelopes88E8C70208D8
22. 16.22 Extrapolation and model singularities472B5CD7929C
23. 16.23 Rooftops and mass inequalities4CC29395A55C
24. 16.24 Divisorial constraints under envelopesA7364A53065E
25. 16.25 Singularity constraints and relative capacity2B1B1CB179EE
26. 16.26 Quantitative rooftop extrapolation5928CB7C3BCE
27. 16.27 Comparison of relative capacitiesDE4415660D60
28. 16.28 Envelopes and volumes of singularities168D3DF32068
    1. 16.28.1 Contact sets840B0858DE95
    2. 16.28.8 Affine growth and projective envelopes6EE0CD52DB46
    3. 16.28.16 Growth slopes and supporting probabilitiesFBAA435459A9
    4. 16.28.31 Variation of continuous weights485B15BBE554
    5. 16.28.42 Local regularity and strict weights5323E094C77D
    6. 16.28.49 A regularization defect along a complex disk924715C5EA1B
    7. 16.28.54 Bounded domination in a semipositive background7A794726C8E7
    8. 16.28.57 Upper and lower volumes879D5A786C1C
    9. 16.28.60 Relative envelope classesE04112C46C03
    10. 16.28.66 Model references and positive mass97D4C0CD199E
    11. 16.28.71 Infinite mass inside the envelope classA211FB2FDF28
29. 16.29 Envelope systems over Hermitian perturbations4AD4DDD929EE
    1. 16.29.1 Curves constant on a left half-line14D1184651D4
    2. 16.29.4 Transition maps and envelope systemsFDD92852ACF2
    3. 16.29.8 The limiting curve and recovery955DE01C09E9
    4. 16.29.12 Changes of representative and limiting massEE5B374433B6
    5. 16.29.15 Failure of recovery in a positive background6596E22FF71B
    6. 16.29.19 Recovery through the Hopf fibration6DDF231D4303
    7. 16.29.23 A nonanalytic family4FE41BF0F18E
    8. 16.29.25 Exact pullback and smooth changes of backgroundE5CE4F64BF58