Trianalytic subvarieties of generalized Kummer varieties

1998/01/09 by D. Kaledin, M. Verbitsky
Mathematics · #math.AG #math.CV #math.DG

paper · pdf

published as Internat. Math. Res. Notices 1998, no. 9, 439--461 · 22 pages, LaTeX 2e

arxiv created 1998/01/09 · arxiv updated 2009/11/30

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 2-dimensional complex torus T, the Hilbert scheme T^[n] classifying zero-dimensional subschemes of T admits a hyperkaehler structure. A finite cover of T^[n] is a product of T and a simply connected hyperkaehler manifold K^[n-1], called generalized Kummer variety. We show that for T generic, the corresponding generalized Kummer variety has no trianalytic subvarieties. This implies that a generic deformation of the generalized Kummer variety has no proper complex subvarieties.

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