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Non-natural non-symplectic involutions on symplectic manifolds of K3^{[2]}-type

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arxiv 1305.6353 v2 pith:QAKCVD76 submitted 2013-05-28 math.AG

Hisanori Ohashi , Malte Wandel This is my paper · ORCID
classification math.AG
keywords involutionstypesmanifoldsnon-symplecticsymplectictypeclassesclassify
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We study non-symplectic involutions on irreducible symplectic manifolds of K3^{[2]}-type with 19 parameters, which is the second largest possible. We classify the conjugacy classes of cohomological representations into four different types and show that there are at most five deformation types, two of which are given by natural involutions and their flops. Next, we give a geometric realisation of one of the new types using moduli spaces of sheaves on K3 surfaces. The geometry of the manifold and the new involution is described in detail.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Analytic torsion for irreducible holomorphic symplectic fourfolds with involution, II: the singularity of the invariant (with an Appendix by Ken-Ichi Yoshikawa)

    math.AG 2024-11 conditional novelty 6.0 of 10

    The singularity of the equivariant analytic torsion invariant on K3[2]-type fourfolds with involution is algebraic, and on Hilbert squares the invariant equals a fixed power of Yoshikawa's K3 invariant up to a constant.

  2. Geometric realizations of non-symplectic involutions on the Hilbert square of a K3 surface

    math.AG 2024-12 conditional novelty 4.0 of 10

    The paper constructs explicit non-symplectic involutions on Hilbert squares of K3 surfaces, including a non-natural involution with invariant lattice <2>⊕<-2>.

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