Chapter 21

Toric and convex geometryFB639626E34C

Convex analysis and pluripotential theory on toric spaces.

Sections and subsections

1. 21.1 Convex analysis and toric potentials4C57CCF28620
2. 21.2 Closed convex functions and supporting slopes5430067C9C99
   1. 21.2.7 Invariant functions on tubes and complex toriEFCDD26ABB1E
3. 21.3 Legendre duality and convex envelopesEC0F5475F1C8
4. 21.4 Slope bodies and bounded growth8CD47210DEE8
5. 21.5 The real Monge–Ampère measure07CCE1F902ED
6. 21.6 Compact convex envelopes and full-mass limits2F45C4BAC276
7. 21.7 Lattice points and volume2479DAC58B22
8. 21.8 Smooth lattice polytopes and projective chartsF916BA03200F
9. 21.9 Fans, divisors and character sectionsFF296752801A
10. 21.10 The Guillemin reference metric256A3051D9FC
11. 21.11 Convex functions and convex bodies9A65EFDDFA3F
    1. 21.11.1 The notion of convex functionsFB8022E8BCA8
    2. 21.11.21 Legendre transform67B012704E18
    3. 21.11.40 Classes of convex functions4F281A03F04D
    4. 21.11.49 Monge–Ampère measuresEAC3497DDCF4
    5. 21.11.59 Several lemmata6F0D797F0564
12. 21.12 Toric pluripotential theory on ample line bundles6F5A4A494129
    1. 21.12.1 Toric setupDD9C13434AA7
    2. 21.12.6 Toric plurisubharmonic functionsE5B138E4CBB0
13. 21.13 Toric pluripotential theory on big line bundlesF1FA15E12648
    1. 21.13.1 Toric setupE05D6993D0C8
    2. 21.13.21 Toric partial Okounkov bodiesE81A302A1530
    3. 21.13.24 Newton bodiesB09F60655D0A
    4. 21.13.31 Partial Okounkov bodies962BB5F87752
    5. 21.13.52 The pluripotential theoryE0A57B09F819
14. 21.14 Hopf fibrations and toric potentials23660BEC4C1F
    1. 21.14.1 Weighted sections on the projective base10355FA4232C
    2. 21.14.3 Descended measures and equations544154BAA081
    3. 21.14.6 Logarithmic coordinates and the gradient simplex11FD5CD723A9