An involution of a projective hyper-Kähler manifold is called antisymplectic if it acts as (-1) on the space of global holomorphic 2-forms. I will present joint work in progress with Laure Flapan, Kieran O'Grady, and Giulia Saccà on antisymplectic involutions associated to polarizations of degree 2. We study the number of connected components of the fixed loci and their geometry.

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