Non-symplectic Involutions on manifolds of K3[n]-type

2019/02/14 by Chiara Camere, Camere, Chiara, Alberto Cattaneo +3 · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Geometric and Algebraic Topology

paper · doi:10.48550/arxiv.1902.05397

Abstract

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≥ 19 and n≤ 5, and provide examples arising as moduli spaces of twisted sheaves on a K3 surface.

Cited by

• On maximality of involutions of hyper-Kähler manifolds and punctual Hilbert schemes of surfaces
• More birational involutions

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