Non-symplectic involutions on manifolds of \(K3^{[n]}\)-type

We study irreducible holomorphic symplectic manifolds deformation equivalent to Hilbert schemes of points on a \(K3\) surface and admitting a non-symplectic involution. We classify the possible discriminant forms of the invariant and anti-invariant lattice for the action of the involution on cohomol...

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Bibliographic Details
Published inarXiv.org
Main Authors Camere, Chiara, Cattaneo, Alberto, Cattaneo, Andrea
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 14.02.2019
Subjects
Deformation
Homology
Invariants
Lattices
Sheaves
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Summary:We study irreducible holomorphic symplectic manifolds deformation equivalent to Hilbert schemes of points on a \(K3\) surface and admitting a non-symplectic involution. We classify the possible discriminant forms of the invariant and anti-invariant lattice for the action of the involution on cohomology, and explicitly describe the lattices in the cases where the invariant has small rank. We also give a modular description of all \(d\)-dimensional families of manifolds of \(K3^{[n]}\)-type with a non-symplectic involution for \(d\geq 19\) and \(n\leq 5\), and provide examples arising as moduli spaces of twisted sheaves on a \(K3\) surface.
ISSN:2331-8422