Birational symplectic manifolds and their deformations

Journal of Differential Geometry

Volumn 45, Issue 3, 1997, Pages 488-513

  Huybrechts, Daniel ^a  

^a MAX PLANCK INSTITUT FÜR MATHEMATIK   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031087004     PISSN: 0022040X     EISSN: 1945743X     Source Type: Journal    
DOI: 10.4310/jdg/1214459840     Document Type: Article

References (26)

1. A. Altman, A. Iarrobino &S. Kleiman, Irreducibility of the compactified Jacobian, Nordic Summer School. Sympos. Math. Oslo, 1976, 1-12.
2. A. Beauville, Variétés Kàhleriermes dont la première classe de Ghern est nulle, J. Differential Geom. 18 (1983) 755-782.
3. A. Beauville, Some remarks on Kàhler manifolds with c = 0, Classification of algebraic and analytic manifolds. Progr. Math. 39 (1983) 1-26.
4. F. Bogomolov, On the decomposition of Kdhler manifolds with trivial canonical class, Math. USSR-Sb. 22 (1974) 580-583.
5. F. Bogomolov, Hamiltonian Kahler manifolds, Sov. Math. Dokl. 19 (1978) 1462-1465.
6. B. Bums &M. Rapoport, On the Torelli problem for Kählerian K3 surfaces, Ann. Sei. École Norm. Sup. 8 (1975) 235-274.
7. I. Debarre, Un contre-exemple au théorème de Torelli pour les variétés symplec-tiques irréductibles, C. R. Acad. Sei. Paris, t. 299, Série 1, 14 (1984) 681-684.
8. I. Fujiki, A theorem on bimeromorphic maps of Köhler manifolds and Its applications, Publ. Res. Inst. Math. Sei. Kyoto Univ. 17 (1981) 735-754.
9. I. Fujiki, On the de Rham cohomology group of a compact Köhler symplectic manifold, Adv. St. Pure Math. 10 (1987) 105-165.
10. A. Fujiki &S. Nakano, Supplement to “On the inverse of monoidal transformation”, Publ. Res. Inst. Math. Sei. Kyoto Univ. 7 (1971) 637-644.
11. L. Göttsche &D. Huybrechts, Hodge numbers of moduli spaces of stable bundles on K3 surfaces, Internat. J. Math. 7 (1996) 359-372.
12. R. Hartshorne, Algebraic geometry, Graduate Texts in Math. Vol. 52, Springer, Berlin, 1977.
13. Y. Kawamata, Unobstructed deformations-A remark on a paper of Z. Ran, J. Algebraic Geom. 1 (1992) 183-190.
14. K. Kodaira &D. Spencer, On deformations of complex analytic structures III. Stability theorems for complex analytic structures, Ann. of Math. 71 (1960) 4376.
15. R. Lazarsfeld, Brill-Noether-Petri without degenerations, J. Differential Geom. 23 (1986) 299-307.
16. T. Matsusaka &D. Mumford, Two fundamental theorems on deformations of polarized varieties, Amer. J. Math. 86 (1964) 668-684.
17. S. Mukai, Symplectic structure of the moduli space of sheaves on an abelian or K3 surface, Invent. Math. 77 (1984) 101-116.
18. S. Mori, On degrees and genera of curves on smooth quartic surfaces in P3, Nagoya Math. J. 96 (1984) 127-132.
19. S. Mukai, Moduli of vector bundles on K3 surfaces, and symplectic manifolds, Sugaku Expositions 1(2) (1988) 138-174.
20. K. O’Grady, The weight-two Hodge structure of moduli spaces of sheaves on a K3 surface, Preprint, 1995.
21. Z. Ran, Deformations of manifolds with torsion or negative canonical bundles, J. Algebraic Geom. 1 (1992) 279-291.
22. P. Samuel, Rational equivalence of arbitrary cycles, Amer. J. Math. 78 (1956) 383-400.
23. G. Scheja, Riemannsche Hebbarkeitssätze für Cohomologieklassen, Math. Ann. 144 (1961) 345-360.
24. G. Tian, Smoothness of the universal deformation space of compact Calabi-Yau manifolds and its Petersson-Weil metric, S. T. Yau, Math. Aspects of String theory, World Scientific, 1987, 629-646.
25. A. N. Todorov, The Weil-Petersson geometry of the moduli space of SU(n >3) (Calabi-Yau) manifolds, Comm. Math. Phys. 126 (1989) 325-346.
26. G. E. Welters, Polarized abelian varieties and the heat eguation, Compositio Math. 49 (1983) 173-194