Deformations of trianalytic subvarieties of hyperkähler manifolds

Selecta Mathematica, New Series

Volumn 4, Issue 3, 1998, Pages 447-490

  Verbitsky, Misha ^a  

^a INSTITUT DES HAUTES ÉTUDES SCIENTIFIQUES   (France)

Author keywords

Hyperholomorphic; Hyperk hler; Real analytic; Singular; Trianalytic

Indexed keywords

EID: 54649083276     PISSN: 10221824     EISSN: 14209020     Source Type: Journal    
DOI: 10.1007/s000290050038     Document Type: Article

References (24)

1. A. Beauville. Variétés Kählériennes dont la première classe de Chern est nulle. J. Diff. Geom. 18 (1983), 755-782.
2. A. Besse. Einstein Manifolds. Springer-Verlag, New York, 1987.
3. E. Calabi. Métriques kähleriennes et fibrés holomorphes. Ann. Ecol. Norm. Sup. 12 (1979), 269-294.
4. P. Deligne. A letter to Carlos Simpson, referred to in [S].
5. A. Douady. Le problème des modules pour les sous-espaces analitiques compactes d'un espace analitique donné. Ann Inst. Fourier 10 (1966), vol 1., 1-95.
6. A. Fujiki. Closedness of the Douady spaces of compact Kähler spaces. Publ. Res. Inst. Math Sci. 14 (1978/79), no. 1, 1-52.
7. H. Grauert and R. Rernmert. Coherent analytic sheaves. Grundlehren der mathematischen Wissenschaften, vol 265. Springer-Verlag, Berlin, 1984.
8. R.E. Greene and H. Wu. Function theory on manifolds inhich possess a pole. Lecture Notes in Mathematics, 699. Springer-Verlag, Berlin, 1979.
9. Ph. Griffiths and J. Harris. Principles of Algebraic Geometry. Wiley-Intersience, New York, 1978.
10. N.J. Hitchin, A. Karlhede, U. Lindström and M. Roček. Hyperkähler metrics and supersymmetry. Comm. Math. Phys. 108 (1987), 535-589.
11. D. Kaledin and M. Verbitsky. Non-Hermitian Yang-Mills connections, alg-geom 9606019 (1996), 48 pages.
12. D. Kaledin and M. Verbitsky. Trianalytic subvarieties of generalized Kummer varieties, math. AG/9801038 (1998), 22 pages.
13. S. Kobayashi. Differential geometry of complex vector bundles. Princeton University Press, 1987.
14. K. Kodaira and D.C. Spencer. On deformations of complex structures II Kodaira K., Collected Works, vol. II. Princeton Univ Press, 1975.
15. D. Lieberman. Compactness of the Chow scheme. Springer Lect. Notes in Math., 670. Springer-Verlag, Berlin, 1978, pp. 140-186.
16. C.T. Simpson. Nonabelian Hodge theory. Proceedings of the International Congress of Mathematicians, Vol. I, II, (Kyoto, 1990). Math. Soc. Japan, Tokyo, 1991, pp. 747-756.
17. G. Stolzenberg. Volumes, Limits and Eoitensions of Analytic Varieties. Lect. Notes in Math., 19. Springer-Verlag, Berlin, 1966.
18. A. Todorov. Moduli of Hyper-Kählerian manifolds I, II. Preprint MPI (1990).
19. K. Uhlenbeck and S.T. Yau. On the existence of Hermitian Yang-Mills connections in stable vector bundles. Comm. on Pure and Appl. Math. 39 (1986), S257-S293.
20. M. Verbitsky. Hyperholornorphic bundles over a hyperkähler manifold, alg-geom electronic preprint 9307008 (1993), 43 pages; also published in: Journ. of Alg. Geom. 5 (1996), no. 4, 633-669.
21. M. Verbitsky. Hyperkahler and holomorphic symplectic geometry I. Electronic preprint alg-geom 9307009 (1993), 14 pages; also published in: Journ. of Alg. Geom. 5 (1996), no. 3, 401-415.
22. M. Verbitsky. Hyperkahler ernbeddings and holomorphic symplectic geometry II. alggeom electronic preprint 9403006 (1994), 14 pages; also published in: GAFA 5 (1995), no. 1, 92-104.
23. M. Verbitsky. Hypercomplex Varieties, alg-geom/9703016 (1997), 40 pages, to appear in Communications in Analysis and Geometry.
24. S.T. Yau. On the Ricci curvature of a compact Kahler manifold and the complex Monge-Ampère equation I. Comm. on Pure and Appl. Math 31 (1978), 339-411.