Chapter 19

Sections, graded series, and Okounkov bodiesA24B3AAE0C3C

Section growth, flags, convex bodies, and almost semigroups.

Sections and subsections

1. 19.1 The theory of Okounkov bodies2DF8DA44EB89
2. 19.2 Almost semigroups1ED20E6196A2
3. 19.3 Flags and valuationsE9A341A325BE
   1. 19.3.1 The algebraic setting07F4BAAD0C8E
   2. 19.3.4 The transcendental settingCA8B57CE6237
4. 19.4 Algebraic partial Okounkov bodiesC9B9B0985C6B
   1. 19.4.1 The spaces of sections41E099D72C80
   2. 19.4.6 Algebraic Okounkov bodiesA81BAAF5B45F
   3. 19.4.15 Construction of partial Okounkov bodies2A53BABD6994
   4. 19.4.25 Basic properties of partial Okounkov bodies1FAA4BD1CBCB
   5. 19.4.40 The Hausdorff convergence propertyB6A67594E2A0
   6. 19.4.50 Recover Lelong numbers from partial Okounkov bodies6EC7E7A8EF44
5. 19.5 Transcendental partial Okounkov bodiesA2D41AECAD65
   1. 19.5.1 The traditional approach to the Okounkov body problemAB52CD73DBE6
   2. 19.5.5 Definitions of partial Okounkov bodies232CC36315A0
   3. 19.5.6 The case of analytic singularities99ECDE21F9AA
   4. 19.5.14 The case of Kähler currents8B697E317627
   5. 19.5.23 The general case101012300A5F
   6. 19.5.31 The valuative characterizationBB37B398D505
6. 19.6 Okounkov test curvesBC31851ECB21
7. 19.7 Almost semigroups00B44728CC57
   1. 19.7.1 Convex bodiesA0D1AD337F41
   2. 19.7.15 The Okounkov bodies of almost semigroupsA31E0D5C79D3
   3. 19.7.16 Generalities on semigroups3A76517E84BF
   4. 19.7.24 Okounkov bodies of semigroupsA6ED691E2495
   5. 19.7.30 Okounkov bodies of almost semigroups10CE70BA2854
8. 19.8 Holomorphic sections and Hermitian mass725C2F97B643
   1. 19.8.1 Weighted sections and Bergman currents5F8226DC1A97
   2. 19.8.4 Gauduchon degree and vanishingE5AAFD4B6553
   3. 19.8.6 Restricted sections and trace dataB7AD9A465882
   4. 19.8.8 Bounded weighted sectionsC9CFDB0867F5
   5. 19.8.10 Section growth on a curve25780F9C24E0
   6. 19.8.12 Homogeneous sections on a Hopf manifold82379C382500
   7. 19.8.14 Section counts and infinite Hermitian massB32BAEE663D4
9. 19.9 Flags, convex bodies and section growth926A00196D5E
   1. 19.9.1 Flag valuations and degree bounds954DDD998705
   2. 19.9.5 The body of a graded section algebraE9A3FA804369
   3. 19.9.8 Intrinsic dimension, lattice and growth72085A67E2A6
   4. 19.9.11 Moishezon manifolds and bounded massF8F1527B70F2
   5. 19.9.14 Flags on a point blowupD45322F36C36
   6. 19.9.18 Curvature rank and section growth1936F96341B0
   7. 19.9.26 The Hopf flag and its lower-dimensional body9B3BD06F2362