Deformations of trianalytic subvarieties of hyperkähler manifolds
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M. Verbitsky [1]
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[1] Institut des Hautes Études Scientifiques
Institut des Hautes Études Scientifiques
Arrondissement de Palaiseau, Francia
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- Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 4, Nº. 3, 1998, págs. 447-490
- Idioma: inglés
- DOI: 10.1007/s000290050038
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Resumen
Let M be a compact complex manifold equipped with a hyperkähler metric, and X be a closed complex analytic subvariety of M. In alg-geom 9403006, we proved that X is trianalytic (i.e., complex analytic with respect to all complex structures induced by the hyperkähler structure), provided that M is generic in its deformation class. Here we study the complex analytic deformations of trianalytic subvarieties. We prove that all deformations of X are trianalytic and naturally isomorphic to X as complex analytic varieties. We show that this isomorphism is compatible with the metric induced from M. Also, we prove that the Douady space of complex analytic deformations of X in M is equipped with a natural hyperkähler structure.
