On the fixed locus of the antisymplectic involution of an EPW cube

2025/05/21 by Francesca Romana Rizzo, Rizzo, Francesca
Computer Science · Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2505.15717

openalex publication_date 2025/05/21 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/30

Abstract

EPW cubes are polarized hyper-Kähler varieties of K3^[3]-type that carry an anti-symplectic involution. We study the geometry of the fixed locus \sW_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--Macrì--O'Grady--Saccà.

Citations

• Non-existence of Enriques manifolds from OG10 type manifolds
• Singularities of Bridgeland moduli spaces for K3 categories: an update
• Atomic objects on hyper-Kähler manifolds
• Derived categories of hyper-Kähler manifolds: extended Mukai vector and integral structure
• Double covers of quadratic degeneracy and Lagrangian intersection loci
• Wall-Crossing implies Brill-Noether. Applications of stability conditions on surfaces
• EPW Cubes
• Projectivity and Birational Geometry of Bridgeland moduli spaces
• Characterizing projective spaces on deformations of Hilbert schemes of K3 surfaces
• Stability conditions on K3 surfaces
• Generators of the cohomology ring of moduli spaces of sheaves on symplectic surfaces

Related

• EPW Cubes
• The geometry of antisymplectic involutions, II
• On the geometry of singular EPW cubes
• Degeneration of natural Lagrangians and Prymian integrable systems
• Theta characteristics and the fixed locus of [-1] on some varieties of Kummer type