Abstract.
Let X be a hyperkähler manifold. Trianalytic subvarieties of X are subvarieties which are complex analytic with respect to all complex structures induced by the hyperkähler structure. Given a K3 surface M, the Hilbert scheme classifying zero-dimensional subschemes of M admits a hyperkähler 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 proper complex subvarieties.
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Submitted: May 1997, Revised version: December 1998
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Verbitsky, M. Trianalytic Subvarieties of the Hilbert Scheme of Points on a K3 Surface. GAFA, Geom. funct. anal. 8, 732–782 (1998). https://doi.org/10.1007/s000390050072
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DOI: https://doi.org/10.1007/s000390050072