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A family of compact complex and symplectic Calabi–Yau manifolds that are non-Kähler

Lizhen Qin and Botong Wang

Geometry & Topology 22 (2018) 2115–2144
Bibliography
1 A Akhmedov, Symplectic Calabi–Yau 6–manifolds, Adv. Math. 262 (2014) 115 MR3228425
2 J Amorós, M Burger, K Corlette, D Kotschick, D Toledo, Fundamental groups of compact Kähler manifolds, 44, Amer. Math. Soc. (1996) MR1379330
3 D Arapura, Geometry of cohomology support loci for local systems, I, J. Algebraic Geom. 6 (1997) 563 MR1487227
4 I K Babenko, I A Taĭmanov, On nonformal simply connected symplectic manifolds, Sibirsk. Mat. Zh. 41 (2000) 253 MR1762178
5 S Baldridge, P Kirk, Coisotropic Luttinger surgery and some new examples of symplectic Calabi–Yau 6–manifolds, Indiana Univ. Math. J. 62 (2013) 1457 MR3188551
6 W Barth, C Peters, A Van de Ven, Compact complex surfaces, 4, Springer (1984) MR749574
7 F A Bogomolov, On Guan’s examples of simply connected non-Kähler compact complex manifolds, Amer. J. Math. 118 (1996) 1037 MR1408498
8 R Bott, L W Tu, Differential forms in algebraic topology, 82, Springer (1982) MR658304
9 M Burger, Fundamental groups of Kähler manifolds and geometric group theory, from: "Séminaire Bourbaki, 2009/2010", Astérisque 339, Soc. Math. France (2011) 305 MR2906358
10 L A Cordero, M Fernández, A Gray, Symplectic manifolds with no Kähler structure, Topology 25 (1986) 375 MR842431
11 P Deligne, P Griffiths, J Morgan, D Sullivan, Real homotopy theory of Kähler manifolds, Invent. Math. 29 (1975) 245 MR0382702
12 A Dimca, Sheaves in topology, Springer (2004) MR2050072
13 M Fernández, M de León, M Saralegui, A six-dimensional compact symplectic solvmanifold without Kähler structures, Osaka J. Math. 33 (1996) 19 MR1381616
14 M Fernández, V Muñoz, Formality of Donaldson submanifolds, Math. Z. 250 (2005) 149 MR2136647
15 M Fernández, V Muñoz, An 8–dimensional nonformal, simply connected, symplectic manifold, Ann. of Math. 167 (2008) 1045 MR2415392
16 J Fine, D Panov, Symplectic Calabi–Yau manifolds, minimal surfaces and the hyperbolic geometry of the conifold, J. Differential Geom. 82 (2009) 155 MR2504773
17 J Fine, D Panov, Hyperbolic geometry and non-Kähler manifolds with trivial canonical bundle, Geom. Topol. 14 (2010) 1723 MR2679581
18 R Friedman, On threefolds with trivial canonical bundle, from: "Complex geometry and Lie theory" (editors J A Carlson, C H Clemens, D R Morrison), Proc. Sympos. Pure Math. 53, Amer. Math. Soc. (1991) 103 MR1141199
19 E Goldstein, S Prokushkin, Geometric model for complex non-Kähler manifolds with SU(3) structure, Comm. Math. Phys. 251 (2004) 65 MR2096734
20 R E Gompf, A new construction of symplectic manifolds, Ann. of Math. 142 (1995) 527 MR1356781
21 G Grantcharov, Geometry of compact complex homogeneous spaces with vanishing first Chern class, Adv. Math. 226 (2011) 3136 MR2764884
22 P Griffiths, J Harris, Principles of algebraic geometry, Wiley (1978) MR507725
23 D Guan, Examples of compact holomorphic symplectic manifolds which are not Kählerian, II, Invent. Math. 121 (1995) 135 MR1345287
24 D Guan, Examples of compact holomorphic symplectic manifolds which are not Kählerian, III, Internat. J. Math. 6 (1995) 709 MR1351162
25 J Gutowski, S Ivanov, G Papadopoulos, Deformations of generalized calibrations and compact non-Kähler manifolds with vanishing first Chern class, Asian J. Math. 7 (2003) 39 MR2015241
26 S Halperin, Lectures on minimal models, 9–10, Soc. Math. France (1983) 261 MR736299
27 P Lu, G Tian, The complex structures on connected sums of S3 × S3, from: "Manifolds and geometry" (editors P de Bartolomeis, F Tricerri, E Vesentini), Sympos. Math. XXXVI, Cambridge Univ. Press (1996) 284 MR1410077
28 G Þ Magnússon, Automorphisms and examples of compact non-Kähler manifolds, preprint (2012) arXiv:1204.3165
29 D McDuff, Examples of simply-connected symplectic non-Kählerian manifolds, J. Differential Geom. 20 (1984) 267 MR772133
30 J W Milnor, J D Stasheff, Characteristic classes, , Princeton Univ. Press (1974) MR0440554
31 J Morrow, K Kodaira, Complex manifolds, Holt, Rinehart and Winston (1971) MR0302937
32 S Papadima, A Suciu, Geometric and algebraic aspects of 1–formality, Bull. Math. Soc. Sci. Math. Roumanie 52(100) (2009) 355 MR2554494
33 S Papadima, A I Suciu, Bieri–Neumann–Strebel–Renz invariants and homology jumping loci, Proc. Lond. Math. Soc. 100 (2010) 795 MR2640291
34 J Park, Non-complex symplectic 4–manifolds with b2+ = 1, Bull. London Math. Soc. 36 (2004) 231 MR2026418
35 I Smith, R P Thomas, S T Yau, Symplectic conifold transitions, J. Differential Geom. 62 (2002) 209 MR1988503
36 W P Thurston, Some simple examples of symplectic manifolds, Proc. Amer. Math. Soc. 55 (1976) 467 MR0402764
37 R Torres, J Yazinski, Geography of symplectic 4– and 6–manifolds, Topology Proc. 46 (2015) 87 MR3224169
38 A Tralle, J Oprea, Symplectic manifolds with no Kähler structure, 1661, Springer (1997) MR1465676
39 L S Tseng, S T Yau, Non-Kähler Calabi–Yau manifolds, from: "String-Math 2011" (editors J Block, J Distler, R Donagi, E Sharpe), Proc. Sympos. Pure Math. 85, Amer. Math. Soc. (2012) 241 MR2985333
40 C Voisin, Hodge structures on cohomology algebras and geometry, Math. Ann. 341 (2008) 39 MR2377469
41 B Wang, Torsion points on the cohomology jump loci of compact Kähler manifolds, Math. Res. Lett. 23 (2016) 545 MR3512898
42 G W Whitehead, Elements of homotopy theory, 61, Springer (1978) MR516508