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

Volume 29
Issue 5, 2251–2782
Issue 4, 1693–2250
Issue 3, 1115–1691
Issue 2, 549–1114
Issue 1, 1–548

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
Orbifold stability and Miyaoka–Yau inequality for minimal pairs

Henri Guenancia and Behrouz Taji

Geometry & Topology 26 (2022) 1435–1482
Bibliography
1 M Artin, Algebraic approximation of structures over complete local rings, Inst. Hautes Études Sci. Publ. Math. 36 (1969) 23 MR268188
2 T Aubin, Équations du type Monge–Ampère sur les variétés kählériennes compactes, Bull. Sci. Math. 102 (1978) 63 MR494932
3 R J Berman, S Boucksom, P Eyssidieux, V Guedj, A Zeriahi, Kähler–Einstein metrics and the Kähler–Ricci flow on log Fano varieties, J. Reine Angew. Math. 751 (2019) 27 MR3956691
4 R J Berman, H Guenancia, Kähler–Einstein metrics on stable varieties and log canonical pairs, Geom. Funct. Anal. 24 (2014) 1683 MR3283927
5 F Campana, H Guenancia, M Păun, Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields, Ann. Sci. École Norm. Sup. 46 (2013) 879 MR3134683
6 F Campana, M Păun, Positivity properties of the bundle of logarithmic tensors on compact Kähler manifolds, Compos. Math. 152 (2016) 2350 MR3577897
7 B Claudon, S Kebekus, B Taji, Generic positivity and applications to hyperbolicity of moduli spaces, from: "Hyperbolicity in algebraic varieties" (editors S Diverio, C Voisin), Panoramas et Synthèses 56, Soc. Math. France (2022) 173
8 H Flenner, Restrictions of semistable bundles on projective varieties, Comment. Math. Helv. 59 (1984) 635 MR780080
9 W Fulton, Intersection theory, 2, Springer (1984) MR732620
10 D Greb, H Guenancia, S Kebekus, Klt varieties with trivial canonical class: holonomy, differential forms, and fundamental groups, Geom. Topol. 23 (2019) 2051 MR3988092
11 D Greb, S Kebekus, S J Kovács, T Peternell, Differential forms on log canonical spaces, Publ. Math. Inst. Hautes Études Sci. 114 (2011) 87 MR2854859
12 D Greb, S Kebekus, T Peternell, B Taji, The Miyaoka–Yau inequality and uniformisation of canonical models, Ann. Sci. École Norm. Sup. 52 (2019) 1487 MR4061021
13 V Guedj, A Zeriahi, The weighted Monge–Ampère energy of quasiplurisubharmonic functions, J. Funct. Anal. 250 (2007) 442 MR2352488
14 H Guenancia, Kähler–Einstein metrics with mixed Poincaré and cone singularities along a normal crossing divisor, Ann. Inst. Fourier (Grenoble) 64 (2014) 1291 MR3330171
15 H Guenancia, Semistability of the tangent sheaf of singular varieties, Algebr. Geom. 3 (2016) 508 MR3568336
16 H Guenancia, M Păun, Conic singularities metrics with prescribed Ricci curvature : general cone angles along normal crossing divisors, J. Differential Geom. 103 (2016) 15 MR3488129
17 H Guenancia, D Wu, On the boundary behavior of Kähler–Einstein metrics on log canonical pairs, Math. Ann. 366 (2016) 101 MR3552234
18 D Huybrechts, M Lehn, The geometry of moduli spaces of sheaves, E31, Friedr. Vieweg & Sohn (1997) MR1450870
19 K Jabbusch, S Kebekus, Families over special base manifolds and a conjecture of Campana, Math. Z. 269 (2011) 847 MR2860268
20 T Jeffres, R Mazzeo, Y A Rubinstein, Kähler–Einstein metrics with edge singularities, Ann. of Math. 183 (2016) 95 MR3432582
21 Y Kawamata, Abundance theorem for minimal threefolds, Invent. Math. 108 (1992) 229 MR1161091
22 R Kobayashi, Kähler–Einstein metric on an open algebraic manifold, Osaka J. Math. 21 (1984) 399 MR752470
23 J Kollár, editor, Flips and abundance for algebraic threefolds, 211, Soc. Math. France (1992) 1 MR1225842
24 J Kollár, Singularities of pairs, from: "Algebraic geometry" (editors J Kollár, R Lazarsfeld, D R Morrison), Proc. Sympos. Pure Math. 62, Amer. Math. Soc. (1997) 221 MR1492525
25 J Kollár, S Mori, Birational geometry of algebraic varieties, 134, Cambridge Univ. Press (1998) MR1658959
26 R Lazarsfeld, Positivity in algebraic geometry, I : Classical setting : line bundles and linear series, 48, Springer (2004) MR2095471
27 R Lazarsfeld, Positivity in algebraic geometry, II : Positivity for vector bundles, and multiplier ideals, 49, Springer (2004) MR2095472
28 G Megyesi, Chern classes of –sheaves, from: "Flips and abundance for algebraic threefolds" (editor J Kollár), Astérisque 211, Soc. Math. France (1992) 115 MR1225842
29 Y Miyaoka, The Chern classes and Kodaira dimension of a minimal variety, from: "Algebraic geometry" (editor T Oda), Adv. Stud. Pure Math. 10, North-Holland (1987) 449 MR946247
30 D Mumford, Towards an enumerative geometry of the moduli space of curves, from: "Arithmetic and geometry, II" (editors M Artin, J Tate), Progr. Math. 36, Birkhäuser (1983) 271 MR717614
31 C T Simpson, Constructing variations of Hodge structure using Yang–Mills theory and applications to uniformization, J. Amer. Math. Soc. 1 (1988) 867 MR944577
32 C T Simpson, Higgs bundles and local systems, Inst. Hautes Études Sci. Publ. Math. 75 (1992) 5 MR1179076
33 J Song, X Wang, The greatest Ricci lower bound, conical Einstein metrics and Chern number inequality, Geom. Topol. 20 (2016) 49 MR3470713
34 G Tian, Kähler–Einstein metrics on algebraic manifolds, from: "Transcendental methods in algebraic geometry" (editors F Catanese, C Ciliberto), Lecture Notes in Math. 1646, Springer (1996) 143 MR1603624
35 G Tian, S T Yau, Existence of Kähler–Einstein metrics on complete Kähler manifolds and their applications to algebraic geometry, from: "Mathematical aspects of string theory" (editor S T Yau), Adv. Ser. Math. Phys. 1, World Sci. (1987) 574 MR915840
36 H Tsuji, Existence and degeneration of Kähler–Einstein metrics on minimal algebraic varieties of general type, Math. Ann. 281 (1988) 123 MR944606
37 S T Yau, Calabi’s conjecture and some new results in algebraic geometry, Proc. Nat. Acad. Sci. U.S.A. 74 (1977) 1798 MR451180
38 S T Yau, On the Ricci curvature of a compact Kähler manifold and the complex Monge–Ampère equation, I, Comm. Pure Appl. Math. 31 (1978) 339 MR480350
39 Y Zhang, Miyaoka–Yau inequality for minimal projective manifolds of general type, Proc. Amer. Math. Soc. 137 (2009) 2749 MR2497488
40 Z Zhang, Scalar curvature bound for Kähler–Ricci flows over minimal manifolds of general type, Int. Math. Res. Not. 2009 (2009) 3901 MR2544732