On the fixed locus of the antisymplectic involution of an EPW cube
Abstract
EPW cubes are polarized hyper-K\"ahler varieties of K3[3]-type that carry an anti-symplectic involution. We study the geometry of the fixed locus A of this involution and prove that it is a rigid atomic Lagrangian submanifold. Our proof is based on a detailed description of certain singular degenerations of EPW cubes and the degeneration methods of Flappan--Macr\`i--O'Grady--Sacc\`a.
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