Fano manifolds of degree ten and EPW sextics

2009/07/16 by Atanas Iliev, Iliev, Atanas, Laurent Manivel +1 · 6 citations
Mathematics · #14D06 #14J40 #14J45 #14K30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · doi:10.48550/arxiv.0907.2781

openalex publication_date 2009/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

O'Grady showed that certain special sextics in ℙ⁵ called EPW sextics admit smooth double covers with a holomorphic symplectic structure. We propose another perspective on these symplectic manifolds, by showing that they can be constructed from the Hilbert schemes of conics on Fano fourfolds of degree ten. As applications, we construct families of Lagrangian surfaces in these symplectic fourfolds, and related integrable systems whose fibers are intermediate Jacobians.

Cited by

• Local structure of the Hilbert scheme of conics in quintic del Pezzo varieties
• Derived categories of Gushel-Mukai surfaces and Fano fourfolds of K3 type
• An atomic criterion for irrationality without quantum computations
• Prime Fano 4-folds with semi-free torus actions
• Projective models for Hilbert squares of K3 surfaces
• More birational involutions

Related

• Lagrangian tens of planes, Enriques surfaces and holomorphic symplectic fourfolds
• Irreducible symplectic 4-folds and Eisenbud-Popescu-Walter sextics
• Dual double EPW-sextics and their periods
• Double covers of EPW-sextics
• Double EPW sextics associated to Gushel-Mukai surfaces