On the fixed locus of the antisymplectic involution of an EPW cube
Algebraic Geometry
2026-02-10 v2
Abstract
EPW cubes are polarized hyper-K\"ahler varieties of K-type that carry an anti-symplectic involution. We study the geometry of the fixed locus of this involution and prove that it is a \emph{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.
Keywords
Cite
@article{arxiv.2505.15717,
title = {On the fixed locus of the antisymplectic involution of an EPW cube},
author = {Francesca Rizzo},
journal= {arXiv preprint arXiv:2505.15717},
year = {2026}
}
Comments
Remark 2.7 added. Comments are welcome!