In this paper we study the second integral cohomology of moduli spaces of semistable sheaves on projective K3 surfaces. If S is a projective K3 surface, v a Mukai vector and H a polarization on S that is general with respect to v, we show that H2(Mv, Z) is a free Z-module of rank 23 carrying a pure weight-two Hodge structure and a lattice structure, with respect to which H2(Mv, Z) is Hodge isometric to the Hodge sublattice v⊥ of the Mukai lattice of S. Similar results are proved for Abelian surfaces.
The second integral cohomology of moduli spaces of sheaves on K3 and Abelian surfaces
Arvid Perego;
2024-01-01
Abstract
In this paper we study the second integral cohomology of moduli spaces of semistable sheaves on projective K3 surfaces. If S is a projective K3 surface, v a Mukai vector and H a polarization on S that is general with respect to v, we show that H2(Mv, Z) is a free Z-module of rank 23 carrying a pure weight-two Hodge structure and a lattice structure, with respect to which H2(Mv, Z) is Hodge isometric to the Hodge sublattice v⊥ of the Mukai lattice of S. Similar results are proved for Abelian surfaces.
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