English

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 K3[3]3^{[3]}-type that carry an anti-symplectic involution. We study the geometry of the fixed locus \sWA\sW_A 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!