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Antisymplectic involutions of holomorphic symplectic manifolds

Abstract : 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.
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Contributor : Arnaud Beauville <>
Submitted on : Friday, November 23, 2012 - 5:01:26 PM
Last modification on : Monday, October 12, 2020 - 10:27:29 AM

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



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