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arXiv · 1010.2607

Symplectic involutions of holomorphic symplectic fourfolds

Chiara Camere
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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.

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Chiara Camere. 2010-10-13. Symplectic involutions of holomorphic symplectic fourfolds. https://doi.org/10.1112/blms%2Fbdr133

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