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 perpendicular to of the Mukai lattice of S. Similar results are proved for Abelian surfaces. (c) 2024 Elsevier Inc. All rights reserved.
Perego, A., Rapagnetta, A. (2024). The second integral cohomology of moduli spaces of sheaves on K3 and Abelian surfaces. ADVANCES IN MATHEMATICS, 440 [10.1016/j.aim.2024.109519].
The second integral cohomology of moduli spaces of sheaves on K3 and Abelian surfaces
Rapagnetta, Antonio
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 perpendicular to of the Mukai lattice of S. Similar results are proved for Abelian surfaces. (c) 2024 Elsevier Inc. All rights reserved.| File | Dimensione | Formato | |
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