Download this article
 Download this article For screen
For printing
Recent Issues

Volume 30
Issue 5, 1611–2042
Issue 4, 1203–1610
Issue 3, 835–1201
Issue 2, 389–833
Issue 1, 1–388

Volume 29, 9 issues

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
 
Author index
To appear
 
Other MSP journals
The volume of pseudoeffective line bundles and partial equilibrium

Tamás Darvas and Mingchen Xia

Geometry & Topology 28 (2024) 1957–1993
Bibliography
1 A Ash, D Mumford, M Rapoport, Y S Tai, Smooth compactifications of locally symmetric varieties, Cambridge Univ. Press (2010) MR2590897
2 E Bedford, B A Taylor, The Dirichlet problem for a complex Monge–Ampère equation, Invent. Math. 37 (1976) 1 MR445006
3 E Bedford, B A Taylor, A new capacity for plurisubharmonic functions, Acta Math. 149 (1982) 1 MR674165
4 R J Berman, Bergman kernels and equilibrium measures for line bundles over projective manifolds, Amer. J. Math. 131 (2009) 1485 MR2559862
5 R Berman, S Boucksom, Growth of balls of holomorphic sections and energy at equilibrium, Invent. Math. 181 (2010) 337 MR2657428
6 R Berman, S Boucksom, D Witt Nyström, Fekete points and convergence towards equilibrium measures on complex manifolds, Acta Math. 207 (2011) 1 MR2863909
7 B Berndtsson, Probability measures associated to geodesics in the space of Kähler metrics, from: "Algebraic and analytic microlocal analysis" (editors M Hitrik, D Tamarkin, B Tsygan, S Zelditch), Springer Proc. Math. Stat. 269, Springer (2018) 395 MR3903321
8 L Bonavero, Inégalités de Morse holomorphes singulières, J. Geom. Anal. 8 (1998) 409 MR1707735
9 A M Botero, J I Burgos Gil, D Holmes, R de Jong, Chern–Weil and Hilbert–Samuel formulae for singular Hermitian line bundles, Doc. Math. 27 (2022) 2563 MR4574244
10 A Botero, J I Burgos Gil, D Holmes, R de Jong, Rings of Siegel–Jacobi forms of bounded relative index are not finitely generated, (2022) arXiv:2203.14583
11 T Bouche, Convergence de la métrique de Fubini–Study d’un fibré linéaire positif, Ann. Inst. Fourier (Grenoble) 40 (1990) 117 MR1056777
12 S Boucksom, Cônes positifs des variétés complexes compactes, PhD thesis, Université Joseph Fourier–Grenoble I (2002)
13 S Boucksom, On the volume of a line bundle, Int. J. Math. 13 (2002) 1043 MR1945706
14 S Boucksom, Singularities of plurisubharmonic functions and multiplier ideals, lecture notes (2017)
15 S Boucksom, C Favre, M Jonsson, Valuations and plurisubharmonic singularities, Publ. Res. Inst. Math. Sci. 44 (2008) 449 MR2426355
16 S Boucksom, P Eyssidieux, V Guedj, A Zeriahi, Monge–Ampère equations in big cohomology classes, Acta Math. 205 (2010) 199 MR2746347
17 J Cao, Numerical dimension and a Kawamata–Viehweg–Nadel-type vanishing theorem on compact Kähler manifolds, Compos. Math. 150 (2014) 1869 MR3279260
18 D Catlin, The Bergman kernel and a theorem of Tian, from: "Analysis and geometry in several complex variables" (editors G Komatsu, M Kuranishi), Birkhäuser (1999) 1 MR1699887
19 U Cegrell, Pluricomplex energy, Acta Math. 180 (1998) 187 MR1638768
20 X Chen, S Sun, Space of Kähler metrics, V : Kähler quantization, from: "Metric and differential geometry" (editors X Dai, X Rong), Progr. Math. 297, Birkhäuser (2012) 19 MR3220438
21 D Coman, G Marinescu, On the first order asymptotics of partial Bergman kernels, Ann. Fac. Sci. Toulouse Math. 26 (2017) 1193 MR3746626
22 D Coman, G Marinescu, V A Nguyên, Holomorphic sections of line bundles vanishing along subvarieties, preprint (2019) arXiv:1909.00328
23 T Darvas, Geometric pluripotential theory on Kähler manifolds, from: "Advances in complex geometry" (editors Y A Rubinstein, B Shiffman), Contemp. Math. 735, Amer. Math. Soc. (2019) 1 MR3996485
24 T Darvas, M Xia, The closures of test configurations and algebraic singularity types, Adv. Math. 397 (2022) 108198 MR4366232
25 T Darvas, E Di Nezza, C H Lu, Monotonicity of nonpluripolar products and complex Monge–Ampère equations with prescribed singularity, Anal. PDE 11 (2018) 2049 MR3812864
26 T Darvas, C H Lu, Y A Rubinstein, Quantization in geometric pluripotential theory, Comm. Pure Appl. Math. 73 (2020) 1100 MR4078714
27 T Darvas, E Di Nezza, H C Lu, The metric geometry of singularity types, J. Reine Angew. Math. 771 (2021) 137 MR4234098
28 J P Demailly, Analytic methods in algebraic geometry, 1, International (2012) MR2978333
29 J P Demailly, On the cohomology of pseudoeffective line bundles, from: "Complex geometry and dynamics" (editors J E Fornæss, M Irgens, E F Wold), Abel Symp. 10, Springer (2015) 51 MR3587462
30 J P Demailly, Extension of holomorphic functions and cohomology classes from non reduced analytic subvarieties, from: "Geometric complex analysis" (editors J Byun, H R Cho, S Y Kim, K H Lee, J D Park), Springer Proc. Math. Stat. 246, Springer (2018) 97 MR3923220
31 J P Demailly, M Paun, Numerical characterization of the Kähler cone of a compact Kähler manifold, Ann. of Math. 159 (2004) 1247 MR2113021
32 J P Demailly, T Peternell, M Schneider, Pseudo-effective line bundles on compact Kähler manifolds, Int. J. Math. 12 (2001) 689 MR1875649
33 E Di Nezza, S Trapani, Monge–Ampère measures on contact sets, Math. Res. Lett. 28 (2021) 1337 MR4471711
34 S K Donaldson, Scalar curvature and projective embeddings, I, J. Differential Geom. 59 (2001) 479 MR1916953
35 Q Guan, X Zhou, A proof of Demailly’s strong openness conjecture, Ann. of Math. 182 (2015) 605 MR3418526
36 V Guedj, A Zeriahi, Intrinsic capacities on compact Kähler manifolds, J. Geom. Anal. 15 (2005) 607 MR2203165
37 V Guedj, A Zeriahi, The weighted Monge–Ampère energy of quasiplurisubharmonic functions, J. Funct. Anal. 250 (2007) 442 MR2352488
38 K Kaveh, A G Khovanskii, Newton–Okounkov bodies, semigroups of integral points, graded algebras and intersection theory, Ann. of Math. 176 (2012) 925 MR2950767
39 D Kim, Equivalence of plurisubharmonic singularities and Siu-type metrics, Monatsh. Math. 178 (2015) 85 MR3384891
40 D Kim, H Seo, Jumping numbers of analytic multiplier ideals, Ann. Polon. Math. 124 (2020) 257 MR4085107
41 Z Lu, On the lower order terms of the asymptotic expansion of Tian–Yau–Zelditch, Amer. J. Math. 122 (2000) 235 MR1749048
42 C H Lu, Comparison of Monge–Ampère capacities, Ann. Polon. Math. 126 (2021) 31 MR4241178
43 C H Lu, V D Nguyen, Degenerate complex Hessian equations on compact Kähler manifolds, Indiana Univ. Math. J. 64 (2015) 1721 MR3436233
44 X Ma, G Marinescu, Holomorphic Morse inequalities and Bergman kernels, 254, Birkhäuser (2007) MR2339952
45 D H Phong, J Sturm, The Monge–Ampère operator and geodesics in the space of Kähler potentials, Invent. Math. 166 (2006) 125 MR2242635
46 J Ross, M Singer, Asymptotics of partial density functions for divisors, J. Geom. Anal. 27 (2017) 1803 MR3667411
47 J Ross, D Witt Nyström, Analytic test configurations and geodesic rays, J. Symplectic Geom. 12 (2014) 125 MR3194078
48 J Ross, D Witt Nyström, Envelopes of positive metrics with prescribed singularities, Ann. Fac. Sci. Toulouse Math. 26 (2017) 687 MR3669969
49 B Runge, Theta functions and Siegel–Jacobi forms, Acta Math. 175 (1995) 165 MR1368246
50 B Shiffman, S Zelditch, Equilibrium distribution of zeros of random polynomials, Int. Math. Res. Not. 2003 (2003) 25 MR1935565
51 J Song, S Zelditch, Bergman metrics and geodesics in the space of Kähler metrics on toric varieties, Anal. PDE 3 (2010) 295 MR2672796
52 J Sun, Asymptotics of partial density function vanishing along smooth subvariety, preprint (2020) arXiv:2010.04951
53 G Tian, Kähler metrics on algebraic manifolds, PhD thesis, Harvard University (1988) MR2636852
54 G Tian, On a set of polarized Kähler metrics on algebraic manifolds, J. Differential Geom. 32 (1990) 99 MR1064867
55 A Trusiani, Kähler–Einstein metrics with prescribed singularities on Fano manifolds, J. Reine Angew. Math. 793 (2022) 1 MR4513162
56 H Tsuji, Extension of log pluricanonical forms from subvarieties, preprint (2007) arXiv:0709.2710
57 D V Vu, Convexity of the class of currents with finite relative energy, Ann. Polon. Math. 128 (2022) 275 MR4437511
58 D Witt Nyström, Monotonicity of nonpluripolar Monge–Ampère masses, Indiana Univ. Math. J. 68 (2019) 579 MR3951074
59 M Xia, Integration by parts formula for non-pluripolar product, preprint (2019) arXiv:1907.06359
60 M Xia, Partial Okounkov bodies and Duistermaat–Heckman measures of non-Archimedean metrics, preprint (2021) arXiv:2112.04290
61 S T Yau, Nonlinear analysis in geometry, Enseign. Math. 33 (1987) 109 MR0896385
62 S Zelditch, Szegő kernels and a theorem of Tian, Int. Math. Res. Not. 1998 (1998) 317 MR1616718
63 S Zelditch, P Zhou, Central limit theorem for spectral partial Bergman kernels, Geom. Topol. 23 (2019) 1961 MR3981005
64 S Zelditch, P Zhou, Interface asymptotics of partial Bergman kernels on S1–symmetric Kähler manifolds, J. Symplectic Geom. 17 (2019) 793 MR4022214
65 K Zhang, A quantization proof of the uniform Yau–Tian–Donaldson conjecture, J. Eur. Math. Soc. (2023)