Trianalytic subvarieties of the Hilbert scheme of points on a K3 surface

Details Trianalytic subvarieties of the Hilbert scheme of points on a K3 surface Trianalytic subvarieties of the Hilbert scheme of points on a K3 surface

1997-05-02

arxiv.org/abs/alg-geom/9705004v2

Geom. Funct. Anal. 8 (1998), no. 4, 732--782

Mathematics

Algebraic Geometry

Arguments improved, errors corrected, rigor added. Sections 8 and 9 were totally rewritten, Tex-type: LaTeX 2e

Scientific paper

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.

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