Artículos de revistas
Any Component Of Moduli Of Polarized Hyperkähler Manifolds Is Dense In Its Deformation Space
Registro en:
Journal Des Mathematiques Pures Et Appliquees. , v. 101, n. 2, p. 188 - 197, 2014.
217824
10.1016/j.matpur.2013.05.008
2-s2.0-84893697284
Autor
Anan'in S.
Verbitsky M.
Institución
Resumen
Let M be a compact hyperkähler manifold, and W the coarse moduli of complex deformations of M. Every positive integer class v in H2(M) defines a divisor Dv in W consisting of all algebraic manifolds polarized by v. We prove that every connected component of this divisor is dense in W. © 2013. 101 2 188 197 Anan'in, S., Grossi, C.H., Coordinate-free classic geometries (2011) Mosc. Math. J., 11, pp. 633-655. , arxiv:math/0702714 Beauville, A., Variétés Kähleriennes dont la première classe de Chern est nulle (1983) J. Differential Geom., 18 (4), pp. 755-782 Besse, A.L., (1987) Einstein Manifolds, p. 516. , Springer-Verlag, Berlin, Heidelberg, New York Bogomolov, F.A., On the decomposition of Kähler manifolds with trivial canonical class (1974) Math. USSR Sb., 22 (4), pp. 580-583 Bogomolov, F.A., Hamiltonian Kähler manifolds (1978) Sov. Math. Dokl., 19, pp. 1462-1465 Boucksom, S., Higher dimensional Zariski decompositions (2004) Ann. Sci. Ec. Norm. Super. (4), 37 (1), pp. 45-76. , arxiv:math/0204336 Demailly, J.-P., Paun, M., Numerical characterization of the Kähler cone of a compact Kähler manifold (2004) Ann. of Math., 159, pp. 1247-1274. , arxiv:math/0105176 Fujiki, A., On the de Rham cohomology group of a compact Kähler symplectic manifold (1987) Adv. Stud. Pure Math., 10, pp. 105-165 Gritsenko, V., Hulek, K., Sankaran, G.K., Moduli spaces of irreducible symplectic manifolds (2010) Compos. Math., 146 (2), pp. 404-434. , arxiv:0802.2078 Gritsenko, V., Hulek, K., Sankaran, G.K., Abelianisation of orthogonal groups and the fundamental group of modulae varieties, p. 21. , arxiv:0810.1614 Huybrechts, D., Compact hyper-Kähler manifolds: basic results (1999) Invent. Math., 135 (1), pp. 63-113. , arxiv:alg-geom/9705025 Huybrechts, D., Finiteness results for hyperkähler manifolds (2003) J. Reine Angew. Math., 558, pp. 15-22. , arxiv:math/0109024 Kamenova, L., Verbitsky, M., Families of Lagrangian fibrations on hyperkaehler manifolds, p. 13. , arxiv:1208.4626 Verbitsky, M., Algebraic structures on hyperkähler manifolds (1996) Math. Res. Lett., 3, pp. 763-767 Verbitsky, M., Trianalytic subvarieties of hyperkaehler manifolds (1995) Geom. Funct. Anal., 5 (1), pp. 92-104 Verbitsky, M., A global Torelli theorem for hyperkähler manifolds, p. 47. , arxiv:0908.4121 Verbitsky, M., Hyperkähler SYZ conjecture and semipositive line bundles (2010) Geom. Funct. Anal., 19 (5), pp. 1481-1493. , arxiv:0811.0639 Verbitsky, M., Parabolic nef currents on hyperkaehler manifolds, p. 19. , arxiv:0907.4217 Vinberg, E.B., Gorbatsevich, V.V., Shvartsman, O.V., Discrete Subgroups of Lie Groups (2000) Encyclopaedia of Mathematical Sciences, 21, p. 224. , Springer-Verlag Viehweg, E., Quasi-projective Moduli for Polarized Manifolds (1995) Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, 30 (BAND). , http://www.uni-due.de/~mat903/books.html, Springer-Verlag, Berlin, Heidelberg, New York, also available at