Geometry & Topology Volume 26, issue 4 (2022)

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Orbifold stability and Miyaoka–Yau inequality for minimal pairs

Henri Guenancia and Behrouz Taji

Geometry & Topology 26 (2022) 1435–1482

DOI: 10.2140/gt.2022.26.1435

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 ℚ–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