Verra Four-Folds, Twisted Sheaves, and the Last Involution. (1st February 2018)

• Record Type: Journal Article
• Authors: Camere, Chiara; Kapustka, Grzegorz; Kapustka, Michał; Mongardi, Giovanni
• Is Part Of: International mathematics research notices. Volume 2019:Number 21(2019)
• Page Start: 6661
• Page End: 6710
• Publication Date: 2018-02-01
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnx327
• Languages: English
• ISSNs: 1073-7928

Abstract

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 K 3 [2] -type admitting non-symplectic involutions with invariant lattices U (2) ⊕ D 4 (−1) or U (2) ⊕ E 8 (−2). This complements the results obtained in [43 ], [13 ], and the results from [29 ] about the geometry of irreducible holomorphic symplectic (IHS) four-folds constructed using the Hilbert scheme of (1, 1) conics on Verra four-folds. As a byproduct we find that IHS four-folds of K 3 [2] -type with Picard lattice U (2) ⊕ E 8 (−2) naturally contain non-nodal Enriques surfaces.