Verra fourfolds, twisted sheaves and the last involution

2017/06/27 by Camere, Chiara, Kapustka, Grzegorz, Kapustka, Michal +1
#14J50 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1706.08955

Abstract

We study the geometry of some moduli spaces of twisted sheaves on K3 surfaces. In particular we introduce induced automorphisms from a K3 surface on moduli spaces of twisted sheaves on this K3 surface. As an application we prove the unirationality of moduli spaces of irreducible holomorphic symplectic manifolds of K3^[2]-type admitting non symplectic involutions with invariant lattices U(2)⊕ D₄(-1) or U(2)⊕ E₈(-2). This complements the results obtained in [Mongardi and Wandel 2015], [Bossiere et al 2016], and the results from [arXiv:1603.00403] about the geometry of IHS fourfolds constructed using the Hilbert scheme of (1,1) conics on Verra fourfolds. As a byproduct we find that IHS fourfolds of K3^[2]-type with Picard lattice U(2)⊕ E₈(-2) naturally contain non-nodal Enriques surfaces.

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