English

Symplectic involutions of holomorphic symplectic fourfolds

Algebraic Geometry 2014-02-26 v1

Abstract

Let X be a holomorphic symplectic fourfold such that b_2=23 and i a symplectic involution of X . The fixed locus F of i is a smooth symplectic submanifold of X; we show that F contains at least 12 isolated points and 1 smooth surface. We conjecture that F is made of 28 isolated fixed points and 1 K3 surface and we provide evidences for the conjecture in some examples, as the Hilbert scheme of a K3 surface, the Fano variety of a cubic in P^5 and the double cover of an EPW sextic.

Keywords

Cite

@article{arxiv.1010.2607,
  title  = {Symplectic involutions of holomorphic symplectic fourfolds},
  author = {Chiara Camere},
  journal= {arXiv preprint arXiv:1010.2607},
  year   = {2014}
}