Trianalytic subvarieties of the Hilbert scheme of points on a K3 surface
alg-geom
2008-02-03 v2 Algebraic Geometry
Abstract
Let X be a hyperkaehler manifold. Trianalytic subvarieties of X are subvarieties which are complex analytic with respect to all complex structures induced by the hyperkaehler structure. Given a K3 surface M, the Hilbert scheme classifying zero-dimensional subschemes of M admits a hyperkaehler structure. We show that for M generic, there are no trianalytic subvarieties of the Hilbert scheme. This implies that a generic deformation of the Hilbert scheme of K3 has no complex subvarieties.
Keywords
Cite
@article{arxiv.alg-geom/9705004,
title = {Trianalytic subvarieties of the Hilbert scheme of points on a K3 surface},
author = {Misha Verbitsky},
journal= {arXiv preprint arXiv:alg-geom/9705004},
year = {2008}
}
Comments
Arguments improved, errors corrected, rigor added. Sections 8 and 9 were totally rewritten, Tex-type: LaTeX 2e