Hodge numbers of moduli spaces of stable bundles on K3 surfaces

Details Hodge numbers of moduli spaces of stable bundles on K3 surfaces Hodge numbers of moduli spaces of stable bundles on K3 surfaces

1994-08-04

arxiv.org/abs/alg-geom/9408001v1

Mathematics

Algebraic Geometry

12 pages, latex

Scientific paper

We show that the Hodge numbers of the moduli space of stable rank two sheaves with primitive determinant on a K3 surface coincide with the Hodge numbers of an appropriate Hilbert scheme of points on the K3 surface. The precise result is: Theorem: Let $X$ be a K3 surface, $L$ a primitive big and nef line bundle and $H$ a generic polarization. If the moduli space of rank two $H$ semi-stable torsion-free sheaves with determiant $L$ and second Chern class $c_2$ has at least dimension 10 then its Hodge numbers coincide with those of the Hilbert scheme of $l:=2c_2-\frac{L^2}{2}-3$ points on $X$.

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