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The fundamental group of compact Kähler threefolds

Benoît Claudon, Andreas Höring and Hsueh-Yung Lin

Geometry & Topology 23 (2019) 3233–3271
Bibliography
1 D Arapura, Homomorphisms between Kähler groups, from: "Topology of algebraic varieties and singularities" (editors J I Cogolludo-Agustín, E Hironaka), Contemp. Math. 538, Amer. Math. Soc. (2011) 95 MR2777817
2 W P Barth, K Hulek, C A M Peters, A Van de Ven, Compact complex surfaces, 4, Springer (2004) MR2030225
3 O Baues, J Riesterer, Virtually abelian Kähler and projective groups, Abh. Math. Semin. Univ. Hambg. 81 (2011) 191 MR2836631
4 A Beauville, Le nombre minimum de fibres singulières d’une courbe stable sur 1, from: "Seminar on pencils of curves of genus at least two", Astérisque 86, Soc. Math. France (1981) 97 MR3618574
5 J Bingener, On deformations of Kähler spaces, I, Math. Z. 182 (1983) 505 MR701367
6 K S Brown, Cohomology of groups, 87, Springer (1982) MR672956
7 Y Brunebarbe, F Campana, Fundamental group and pluridifferentials on compact Kähler manifolds, Mosc. Math. J. 16 (2016) 651 MR3598500
8 N Buchdahl, Algebraic deformations of compact Kähler surfaces, Math. Z. 253 (2006) 453 MR2221080
9 N Buchdahl, Algebraic deformations of compact Kähler surfaces, II, Math. Z. 258 (2008) 493 MR2369040
10 F Campana, Remarques sur le revêtement universel des variétés kählériennes compactes, Bull. Soc. Math. France 122 (1994) 255 MR1273904
11 F Campana, Negativity of compact curves in infinite covers of projective surfaces, J. Algebraic Geom. 7 (1998) 673 MR1642728
12 F Campana, Orbifolds, special varieties and classification theory, Ann. Inst. Fourier (Grenoble) 54 (2004) 499 MR2097416
13 F Campana, Orbifoldes géométriques spéciales et classification biméromorphe des variétés kählériennes compactes, J. Inst. Math. Jussieu 10 (2011) 809 MR2831280
14 F Campana, B Claudon, Abelianity conjecture for special compact Kähler 3–folds, Proc. Edinb. Math. Soc. 57 (2014) 55 MR3165012
15 F Campana, B Claudon, P Eyssidieux, Représentations linéaires des groups kählériens et de leurs analogues projectifs, J. Éc. polytech. Math. 1 (2014) 331 MR322791
16 F Campana, B Claudon, P Eyssidieux, Représentations linéaires des groupes kählériens : factorisations et conjecture de Shafarevich linéaire, Compos. Math. 151 (2015) 351 MR3314830
17 F Campana, T Peternell, Complex threefolds with non-trivial holomorphic 2–forms, J. Algebraic Geom. 9 (2000) 223 MR1735771
18 F Campana, Q Zhang, Compact Kähler threefolds of π1–general type, from: "Recent progress in arithmetic and algebraic geometry" (editors Y Kachi, S B Mulay, P Tzermias), Contemp. Math. 386, Amer. Math. Soc. (2005) 1 MR2182767
19 B Claudon, Invariance de la Γ–dimension pour certaines familles kählériennes de dimension 3, Math. Z. 266 (2010) 265 MR2678627
20 B Claudon, Smooth families of tori and linear Kähler groups, Ann. Fac. Sci. Toulouse Math. 27 (2018) 477 MR3869072
21 J P Demailly, Mesures de Monge–Ampère et caractérisation géométrique des variétés algébriques affines, 19, Soc. Math. France (1985) 124 MR813252
22 H Flenner, S Kosarew, On locally trivial deformations, Publ. Res. Inst. Math. Sci. 23 (1987) 627 MR918518
23 A Fujiki, Closedness of the Douady spaces of compact Kähler spaces, Publ. Res. Inst. Math. Sci. 14 (1978) 1 MR0486648
24 O Fujino, S Mori, A canonical bundle formula, J. Differential Geom. 56 (2000) 167 MR1863025
25 P Graf, Algebraic approximation of Kähler threefolds of Kodaira dimension zero, Math. Ann. 371 (2018) 487 MR3788856
26 H Grauert, Über Modifikationen und exzeptionelle analytische Mengen, Math. Ann. 146 (1962) 331 MR137127
27 D Greb, S Kebekus, S J Kovács, Extension theorems for differential forms and Bogomolov–Sommese vanishing on log canonical varieties, Compos. Math. 146 (2010) 193 MR2581247
28 R Hartshorne, Algebraic geometry, 52, Springer (1977) MR0463157
29 A Höring, T Peternell, Minimal models for Kähler threefolds, Invent. Math. 203 (2016) 217 MR3437871
30 B Iversen, Cohomology of sheaves, Springer (1986) MR842190
31 K Kodaira, On compact complex analytic surfaces, I, Ann. of Math. 71 (1960) 111 MR132556
32 K Kodaira, On compact analytic surfaces, II, Ann. of Math. 77 (1963) 563 MR0184257
33 K Kodaira, On compact analytic surfaces, III, Ann. of Math. 78 (1963) 1 MR0184257
34 J Kollár, Shafarevich maps and plurigenera of algebraic varieties, Invent. Math. 113 (1993) 177 MR1223229
35 J Kollár, Lectures on resolution of singularities, 166, Princeton Univ. Press (2007) MR2289519
36 R Lazarsfeld, Positivity in algebraic geometry, I : Classical setting — line bundles and linear series, 48, Springer (2004) MR2095471
37 H Y Lin, Algebraic approximations of compact Kähler threefolds, preprint (2017) arXiv:1710.01083
38 H Y Lin, Algebraic approximations of fibrations in abelian varieties over a curve, preprint (2018) arXiv:1612.09271
39 N Nakayama, On Weierstrass models, from: "Algebraic geometry and commutative algebra, II" (editors H Hijikata, H Hironaka, M Maruyama, H Matsumura, M Miyanishi, T Oda, K Ueno), Kinokuniya (1988) 405 MR977771
40 N Nakayama, Global structure of an elliptic fibration, Publ. Res. Inst. Math. Sci. 38 (2002) 451 MR1918053
41 N Nakayama, Local structure of an elliptic fibration, from: "Higher dimensional birational geometry" (editors S Mori, Y Miyaoka), Adv. Stud. Pure Math. 35, Math. Soc. Japan (2002) 185 MR1929795
42 Y Namikawa, Extension of 2–forms and symplectic varieties, J. Reine Angew. Math. 539 (2001) 123 MR1863856
43 E Sernesi, Deformations of algebraic schemes, 334, Springer (2006) MR2247603
44 J P Serre, Sur la topologie des variétés algébriques en caractéristique p, from: "Symposium internacional de topología algebraica International symposium on algebraic topology", Universidad Nacional Autónoma de México (1958) 24 MR0098097
45 Y T Siu, Strong rigidity for Kähler manifolds and the construction of bounded holomorphic functions, from: "Discrete groups in geometry and analysis" (editor R Howe), Progr. Math. 67, Birkhäuser (1987) 124 MR900825
46 S Takayama, Local simple connectedness of resolutions of log-terminal singularities, Internat. J. Math. 14 (2003) 825 MR2013147
47 K Ueno, Classification theory of algebraic varieties and compact complex spaces, 439, Springer (1975) MR0506253
48 C Voisin, Théorie de Hodge et géométrie algébrique complexe, 10, Soc. Math. France (2002) MR1988456
49 C Voisin, On the homotopy types of compact Kähler and complex projective manifolds, Invent. Math. 157 (2004) 329 MR2076925
50 C Voisin, On the homotopy types of Kähler manifolds and the birational Kodaira problem, J. Differential Geom. 72 (2006) 43 MR2215455
51 J Włodarczyk, Resolution of singularities of analytic spaces, from: "Proceedings of Gökova Geometry–Topology Conference 2008" (editors S Akbulut, T Önder, R J Stern), GGT (2009) 31 MR2500573
52 S Zucker, Hodge theory with degenerating coefficients : L2 cohomology in the Poincaré metric, Ann. of Math. 109 (1979) 415 MR534758