Deformations of trianalytic subvarieties of hyperkähler manifolds
| dc.creator | Verbitsky, Misha | |
| dc.date | 1996-10-09 | |
| dc.date.accessioned | 2026-07-07T09:07:00Z | |
| dc.date.available | 2026-07-07T09:07:00Z | |
| dc.description | 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. | |
| dc.description | 51 pages, LaTeX2e | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9610010 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9610010 | |
| dc.identifier | Selecta Math. (N.S.) 4 (1998), no. 3, 447--490. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150218 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Deformations of trianalytic subvarieties of hyperkähler manifolds | |
| dc.type | text |