Verra Four-Folds, Twisted Sheaves, and the Last Involution-Reference-Cited by-同舟云学术

Verra Four-Folds, Twisted Sheaves, and the Last Involution

Published:2018-02-01 Issue:21 Volume:2019 Page:6661-6710
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Camere Chiara¹,Kapustka Grzegorz²,Kapustka Michał³⁴,Mongardi Giovanni⁵

Affiliation:

1. Dipartimento di Matematica, Università degli Studi di Milano, Milano, Italy

2. Department of Mathematics and Informatics, Jagiellonian University, Poland and University of Zürich

3. Department of Mathematics and Natural Sciences, University of Stavanger, Stavanger, Norway

4. Department of Mathematics and Informatics, Jagiellonian University, Kraków, Poland

5. Dipartimento di Matematica, Alma Mater Studiorum Università di Bologna, Bologna, Italy

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 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 [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 K3[2]-type with Picard lattice U(2) ⊕ E8(−2) naturally contain non-nodal Enriques surfaces.

Funder

NCN

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2019/21/6661/34906648/rnx327.pdf

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