Antisymplectic involutions of holomorphic symplectic manifolds

Arnaud Beauville (1)

1 JAD - Laboratoire Jean Alexandre Dieudonné

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 Â-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.

Domaines: Géométrie algébrique [math.AG]

Arnaud Beauville. Antisymplectic involutions of holomorphic symplectic manifolds. Journal of topology, 2011, 4 (2), pp.300-304. ⟨10.1112/jtopol/jtr002⟩. ⟨hal-00756786⟩