Geometry & Topology Volume 23, issue 4 (2019)

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Klt varieties with trivial canonical class: holonomy, differential forms, and fundamental groups

Daniel Greb, Henri Guenancia and Stefan Kebekus

Geometry & Topology 23 (2019) 2051–2124

DOI: 10.2140/gt.2019.23.2051

Bibliography

1	D Arapura, Higgs bundles, integrability, and holomorphic forms, from: "Motives, polylogarithms and Hodge theory, II" (editors F Bogomolov, L Katzarkov), Int. Press Lect. Ser. 3, International (2002) 605 MR1978714
2	V Balaji, J Kollár, Holonomy groups of stable vector bundles, Publ. Res. Inst. Math. Sci. 44 (2008) 183 MR2426347
3	A Beauville, Some remarks on Kähler manifolds with c₁ = 0, from: "Classification of algebraic and analytic manifolds" (editor K Ueno), Progr. Math. 39, Birkhäuser (1983) 1 MR728605
4	A Beauville, Variétés Kähleriennes dont la première classe de Chern est nulle, J. Differential Geom. 18 (1983) 755 MR730926
5	A J Berrick, Groups with no nontrivial linear representations, Bull. Austral. Math. Soc. 50 (1994) 1 MR1285653
6	A L Besse, Einstein manifolds, 10, Springer (1987) MR867684
7	C Birkar, P Cascini, C D Hacon, J McKernan, Existence of minimal models for varieties of log general type, J. Amer. Math. Soc. 23 (2010) 405 MR2601039
8	S Boucksom, P Eyssidieux, V Guedj, editors, An introduction to the Kähler–Ricci flow, 2086, Springer (2013) MR3202578
9	T Bröcker, T tom Dieck, Representations of compact Lie groups, 98, Springer (1985) MR781344
10	Y Brunebarbe, B Klingler, B Totaro, Symmetric differentials and the fundamental group, Duke Math. J. 162 (2013) 2797 MR3127814
11	D Bump, Lie groups, 225, Springer (2004) MR2062813
12	F Campana, On twistor spaces of the class 𝒞, J. Differential Geom. 33 (1991) 541 MR1094468
13	F Campana, Fundamental group and positivity of cotangent bundles of compact Kähler manifolds, J. Algebraic Geom. 4 (1995) 487 MR1325789
14	F Campana, H Guenancia, M Păun, Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields, Ann. Sci. Éc. Norm. Supér. 46 (2013) 879 MR3134683
15	P Cascini, G L Nave, Kähler–Ricci flow and the minimal model program for projective varieties, preprint (2006) arXiv:math/0603064v1
16	J P Demailly, Complex analytic and differential geometry, book project (2012)
17	J P Demailly, N Pali, Degenerate complex Monge–Ampère equations over compact Kähler manifolds, Internat. J. Math. 21 (2010) 357 MR2647006
18	G Dethloff, H Grauert, Seminormal complex spaces, from: "Several complex variables, VII" (editors H Grauert, T Peternell, R Remmert), Encyclopaedia Math. Sci. 74, Springer (1994) 183 MR1326621
19	S Druel, A decomposition theorem for singular spaces with trivial canonical class of dimension at most five, Invent. Math. 211 (2018) 245 MR3742759
20	P Eyssidieux, V Guedj, A Zeriahi, Singular Kähler–Einstein metrics, J. Amer. Math. Soc. 22 (2009) 607 MR2505296
21	F F Favale, Calabi–Yau quotients with terminal singularities, Boll. Unione Mat. Ital. 11 (2018) 55 MR3782691
22	W Fulton, J Harris, Representation theory: a first course, 129, Springer (1991) MR1153249
23	W Fulton, R Lazarsfeld, Connectivity and its applications in algebraic geometry, from: "Algebraic geometry" (editors A Libgober, P Wagreich), Lecture Notes in Mathematics 862, Springer (1981) 26 MR644817
24	R Goodman, N R Wallach, Symmetry, representations, and invariants, 255, Springer (2009) MR2522486
25	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
26	D Greb, S Kebekus, T Peternell, Reflexive differential forms on singular spaces. Geometry and cohomology, J. Reine Angew. Math. 697 (2014) 57 MR3281652
27	D Greb, S Kebekus, T Peternell, Étale fundamental groups of Kawamata log terminal spaces, flat sheaves, and quotients of abelian varieties, Duke Math. J. 165 (2016) 1965 MR3522654
28	D Greb, S Kebekus, T Peternell, Movable curves and semistable sheaves, Int. Math. Res. Not. 2016 (2016) 536 MR3493425
29	D Greb, S Kebekus, T Peternell, Singular spaces with trivial canonical class, from: "Minimal models and extremal rays" (editors J Kollár, O Fujino, S Mukai, N Nakayama), Adv. Stud. Pure Math. 70, Math. Soc. Japan (2016) 67 MR3617779
30	A Grothendieck, Représentations linéaires et compactification profinie des groupes discrets, Manuscripta Math. 2 (1970) 375 MR0262386
31	A Grothendieck, Revêtements étales et groupe fondamental (SGA 1), 224, Springer (1971) MR0354651
32	V Guedj, A Zeriahi, The weighted Monge–Ampère energy of quasiplurisubharmonic functions, J. Funct. Anal. 250 (2007) 442 MR2352488
33	H Guenancia, Semistability of the tangent sheaf of singular varieties, Algebr. Geom. 3 (2016) 508 MR3568336
34	R C Gunning, Introduction to holomorphic functions of several variables, III : Homological theory, Wadsworth and Brooks/Cole (1990) MR1059457
35	R Hartshorne, Algebraic geometry, 52, Springer (1977) MR0463157
36	A Höring, T Peternell, Algebraic integrability of foliations with numerically trivial canonical bundle, Invent. Math. 216 (2019) 395 MRMR3953506
37	D Huybrechts, M Lehn, The geometry of moduli spaces of sheaves, Cambridge Univ. Press (2010) MR2665168
38	D D Joyce, Compact manifolds with special holonomy, Oxford Univ. Press (2000) MR1787733
39	D Kaledin, M Lehn, C Sorger, Singular symplectic moduli spaces, Invent. Math. 164 (2006) 591 MR2221132
40	B Kleiner, A new proof of Gromov’s theorem on groups of polynomial growth, J. Amer. Math. Soc. 23 (2010) 815 MR2629989
41	B Klingler, Symmetric differentials, Kähler groups and ball quotients, Invent. Math. 192 (2013) 257 MR3044124
42	S Kobayashi, The first Chern class and holomorphic symmetric tensor fields, J. Math. Soc. Japan 32 (1980) 325 MR567422
43	S Kobayashi, Differential geometry of complex vector bundles, 15, Princeton Univ. Press (1987) MR909698
44	S Kobayashi, K Nomizu, Foundations of differential geometry, I, Wiley (1996) MR1393940
45	J Kollár, Shafarevich maps and automorphic forms, Princeton Univ. Press (1995) MR1341589
46	J Kollár, S Mori, Birational geometry of algebraic varieties, 134, Cambridge Univ. Press (1998) MR1658959
47	S Kołodziej, The complex Monge–Ampère equation, Acta Math. 180 (1998) 69 MR1618325
48	R Lazarsfeld, Positivity in algebraic geometry, I : Classical setting : line bundles and linear series, 48, Springer (2004) MR2095471
49	D Matsushita, On base manifolds of Lagrangian fibrations, Sci. China Math. 58 (2015) 531 MR3319924
50	N Nakayama, Zariski-decomposition and abundance, 14, Math. Soc. Japan (2004) MR2104208
51	Y Namikawa, A note on symplectic singularities, preprint (2001) arXiv:math/0101028
52	K Oguiso, J Sakurai, Calabi–Yau threefolds of quotient type, Asian J. Math. 5 (2001) 43 MR1868164
53	K Oguiso, S Schröer, Enriques manifolds, J. Reine Angew. Math. 661 (2011) 215 MR2863907
54	K Oguiso, D Q Zhang, On the most algebraic K3 surfaces and the most extremal log Enriques surfaces, Amer. J. Math. 118 (1996) 1277 MR1420924
55	A Perego, A Rapagnetta, The moduli spaces of sheaves on K3 surfaces are irreducible symplectic varieties, preprint (2018) arXiv:1802.01182
56	T Peternell, Minimal varieties with trivial canonical classes, I, Math. Z. 217 (1994) 377 MR1306667
57	M Păun, Regularity properties of the degenerate Monge–Ampère equations on compact Kähler manifolds, Chin. Ann. Math. Ser. B 29 (2008) 623 MR2470619
58	R Schoen, S T Yau, Lectures on differential geometry, I, International (1994) MR1333601
59	S Takayama, Local simple connectedness of resolutions of log-terminal singularities, Internat. J. Math. 14 (2003) 825 MR2013147
60	G Tian, Kähler–Einstein metrics on algebraic manifolds, from: "Transcendental methods in algebraic geometry" (editors F Catanese, C Ciliberto), Lecture Notes in Mathematics 1646, Springer (1996) 143 MR1603624
61	G Tian, Z Zhang, On the Kähler–Ricci flow on projective manifolds of general type, Chinese Ann. Math. Ser. B 27 (2006) 179 MR2243679
62	H Tsuji, Existence and degeneration of Kähler–Einstein metrics on minimal algebraic varieties of general type, Math. Ann. 281 (1988) 123 MR944606
63	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
64	Z Zhang, On degenerate Monge–Ampère equations over closed Kähler manifolds, Int. Math. Res. Not. 2006 (2006) MR2233716