We study irreducible holomorphic symplectic manifolds deformation equivalent to Hilbert schemes of points on a surface and admitting a non-symplectic involution. We classify the possible discriminant quadratic forms of the invariant and coinvariant lattice for the action of the involution on cohomology and explicitly describe the lattices in the cases where the invariant lattice has small rank. We also give a modular description of all -dimensional families of manifolds of -type with a non-symplectic involution for and and provide examples arising as moduli spaces of twisted sheaves on a surface.
NON-SYMPLECTIC INVOLUTIONS on MANIFOLDS of K3^{[n]}-TYPE / Camere, C.; Cattaneo, A.; Cattaneo, A.. - In: NAGOYA MATHEMATICAL JOURNAL. - ISSN 0027-7630. - 243:(2021), pp. 278-302. [10.1017/nmj.2019.43]
NON-SYMPLECTIC INVOLUTIONS on MANIFOLDS of K3^{[n]}-TYPE
Cattaneo A.;
2021-01-01
Abstract
We study irreducible holomorphic symplectic manifolds deformation equivalent to Hilbert schemes of points on a surface and admitting a non-symplectic involution. We classify the possible discriminant quadratic forms of the invariant and coinvariant lattice for the action of the involution on cohomology and explicitly describe the lattices in the cases where the invariant lattice has small rank. We also give a modular description of all -dimensional families of manifolds of -type with a non-symplectic involution for and and provide examples arising as moduli spaces of twisted sheaves on a surface.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
