Deformations of trianalytic subvarieties of hyperkähler manifolds

dc.creatorVerbitsky, Misha
dc.date1996-10-09
dc.date.accessioned2026-07-07T09:07:00Z
dc.date.available2026-07-07T09:07:00Z
dc.descriptionLet $M$ 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.
dc.description51 pages, LaTeX2e
dc.identifierhttps://arxiv.org/abs/alg-geom/9610010
dc.identifierhttp://arxiv.org/abs/alg-geom/9610010
dc.identifierSelecta Math. (N.S.) 4 (1998), no. 3, 447--490.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/150218
dc.subjectAlgebraic Geometry
dc.titleDeformations of trianalytic subvarieties of hyperkähler manifolds
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