Volume 23, issue 4 (2019)

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
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
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