Hodge numbers of moduli spaces of stable bundles on K3 surfaces

Abstract

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 $X$.

12 pages, latex

References in corpus (1)

• Stable pairs on curves and surfaces

Cited by in corpus (3)

• Stability conditions on Kuznetsov components
• Irreducibility of the moduli space of vector bundles on surfaces and Brill-Noether theory on singular curves
• Some notes on the moduli of stable sheaves on elliptic surfaces