Antisymplectic involutions of holomorphic symplectic manifolds

Details Antisymplectic involutions of holomorphic symplectic manifolds Antisymplectic involutions of holomorphic symplectic manifolds

2010-08-18

arxiv.org/abs/1008.3108v3

Mathematics

Algebraic Geometry

Final version, accepted for publication by the Journal of Topology

Scientific paper

Let X be a holomorphic symplectic manifold, of dimension divisible by 4, and
s an antisymplectic involution of X . The fixed locus F of s is a Lagrangian
submanifold of X ; we show that its \^A-genus is 1. As an application, we
determine all possibilities for the Chern numbers of F when X is a deformation
of the Hilbert square of a K3 surface.

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