Geometry & Topology Volume 21, issue 2 (2017)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Rational cohomology tori

Olivier Debarre, Zhi Jiang and Martí Lahoz

Appendix: William F Sawin

Geometry & Topology 21 (2017) 1095–1130

DOI: 10.2140/gt.2017.21.1095

Bibliography

1	D Abramovich, J Wang, Equivariant resolution of singularities in characteristic 0, Math. Res. Lett. 4 (1997) 427 MR1453072
2	V Ancona, B Gaveau, Differential forms on singular varieties: de Rham and Hodge theory simplified, 273, Chapman & Hall/CRC (2006) MR2168647
3	A Blanchard, Sur les variétés analytiques complexes, Ann. Sci. Ecole Norm. Sup. 73 (1956) 157 MR0087184
4	F A Bogomolov, C Böhning, H C G von Bothmer, Birationally isotrivial fiber spaces, Eur. J. Math. 2 (2016) 45 MR3454089
5	R Bott, L W Tu, Differential forms in algebraic topology, 82, Springer (1982) MR658304
6	G E Bredon, Introduction to compact transformation groups, 46, Academic Press (1972) MR0413144
7	F Catanese, Moduli and classification of irregular Kaehler manifolds (and algebraic varieties) with Albanese general type fibrations, Invent. Math. 104 (1991) 263 MR1098610
8	F Catanese, Topological methods in moduli theory, Bull. Math. Sci. 5 (2015) 287 MR3404712
9	J A Chen, O Debarre, Z Jiang, Varieties with vanishing holomorphic Euler characteristic, J. Reine Angew. Math. 691 (2014) 203 MR3213551
10	J A Chen, C D Hacon, Pluricanonical maps of varieties of maximal Albanese dimension, Math. Ann. 320 (2001) 367 MR1839768
11	J A Chen, C D Hacon, On the irregularity of the image of the Iitaka fibration, Comm. Algebra 32 (2004) 203 MR2036231
12	J A Chen, Z Jiang, Positivity in varieties of maximal Albanese dimension, J. Reine Angew. Math. (2015)
13	J Chen, Z Jiang, Z Tian, Irregular varieites with geometric genus one, theta divisors, and fake tori, preprint (2016) arXiv:1604.07503
14	O Debarre, Cohomological characterizations of the complex projective space, preprint (2015) arXiv:1512.04321
15	P Deligne, Théorie de Hodge, III, Inst. Hautes Études Sci. Publ. Math. 44 (1974) 5 MR0498552
16	L Ein, R Lazarsfeld, Singularities of theta divisors and the birational geometry of irregular varieties, J. Amer. Math. Soc. 10 (1997) 243 MR1396893
17	A Fujiki, Closedness of the Douady spaces of compact Kähler spaces, Publ. Res. Inst. Math. Sci. 14 (1978/79) 1 MR0486648
18	A Fujiki, Duality of mixed Hodge structures of algebraic varieties, Publ. Res. Inst. Math. Sci. 16 (1980) 635 MR602463
19	T Fujita, On Kähler fiber spaces over curves, J. Math. Soc. Japan 30 (1978) 779 MR513085
20	T Fujita, On topological characterizations of complex projective spaces and affine linear spaces, Proc. Japan Acad. Ser. A Math. Sci. 56 (1980) 231 MR580087
21	M Green, R Lazarsfeld, Deformation theory, generic vanishing theorems, and some conjectures of Enriques, Catanese and Beauville, Invent. Math. 90 (1987) 389 MR910207
22	M Green, R Lazarsfeld, Higher obstructions to deforming cohomology groups of line bundles, J. Amer. Math. Soc. 4 (1991) 87 MR1076513
23	C D Hacon, A derived category approach to generic vanishing, J. Reine Angew. Math. 575 (2004) 173 MR2097552
24	F Hirzebruch, K Kodaira, On the complex projective spaces, J. Math. Pures Appl. 36 (1957) 201 MR0092195
25	Z Jiang, M Lahoz, S Tirabassi, On the Iitaka fibration of varieties of maximal Albanese dimension, Int. Math. Res. Not. 2013 (2013) 2984 MR3072998
26	Z Jiang, Q Yin, On the Chow ring of certain rational cohomology tori, preprint (2016) arXiv:1603.01426
27	Y Kawamata, Characterization of abelian varieties, Compositio Math. 43 (1981) 253 MR622451
28	S J Kovács, Rational, log canonical, Du Bois singularities : on the conjectures of Kollár and Steenbrink, Compositio Math. 118 (1999) 123 MR1713307
29	S J Kovács, A characterization of rational singularities, Duke Math. J. 102 (2000) 187 MR1749436
30	S J Kovács, K E Schwede, Hodge theory meets the minimal model program : a survey of log canonical and Du Bois singularities, from: "Topology of stratified spaces" (editors G Friedman, E Hunsicker, A Libgober, L Maxim), Math. Sci. Res. Inst. Publ. 58, Cambridge Univ. Press (2011) 51 MR2796408
31	A S Libgober, J W Wood, Uniqueness of the complex structure on Kähler manifolds of certain homotopy types, J. Differential Geom. 32 (1990) 139 MR1064869
32	J A Morrow, A survey of some results on complex Kähler manifolds, from: "Global analysis : papers in honor of K Kodaira" (editors D C Spencer, S Iyanaga), Univ. Tokyo Press (1969) 315 MR0258072
33	R Pardini, Abelian covers of algebraic varieties, J. Reine Angew. Math. 417 (1991) 191 MR1103912
34	R Pardini, Infinitesimal Torelli and abelian covers of algebraic surfaces, from: "Problems in the theory of surfaces and their classification" (editors F Catanese, C Ciliberto, M Cornalba), Sympos. Math. XXXII, Academic Press (1991) 247 MR1273381
35	C A M Peters, J H M Steenbrink, Mixed Hodge structures, 52, Springer (2008) MR2393625
36	M Popa, C Schnell, Kodaira dimension and zeros of holomorphic one-forms, Ann. of Math. 179 (2014) 1109 MR3171760
37	C Simpson, Subspaces of moduli spaces of rank one local systems, Ann. Sci. École Norm. Sup. 26 (1993) 361 MR1222278
38	K Ueno, Classification theory of algebraic varieties and compact complex spaces, 439, Springer (1975) MR0506253
39	K Ueno, Bimeromorphic geometry of algebraic and analytic threefolds, from: "Algebraic threefolds" (editor A Conte), Lecture Notes in Math. 947, Springer (1982) 1 MR672613
40	E Viehweg, Weak positivity and the additivity of the Kodaira dimension for certain fibre spaces, from: "Algebraic varieties and analytic varieties" (editor S Iitaka), Adv. Stud. Pure Math. 1, North-Holland (1983) 329 MR715656