Dual double EPW-sextics and their periods

2006/05/03 by Kieran G. O’Grady, O'Grady, Kieran G. · 2 citations
Mathematics · #14C30 #14J35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0605085

openalex publication_date 2006/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A locally complete family of projective symplectic 4-folds is provided by natural double covers of Eisenbud-Popescu-Walter (EPW) sextic hypersurfaces in projective 5-space. The dual of an EPW sextic is another EPW sextic, thus to a double EPW sextic X we may associate a "dual" double EPW sextic X^\vee. We show how to obtain the Hodge structure on H²(X^\vee) from that on H²(X); it turns out that they are isomorphic over the rationals but not over the integers (in general).

Cited by

• EPW varieties as moduli spaces on ordinary GM surfaces and special GM threefolds
• Derived categories of Gushel-Mukai surfaces and Fano fourfolds of K3 type

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• EPW-sextics: taxonomy
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