Dual double EPW-sextics and their periods

Details Dual double EPW-sextics and their periods Dual double EPW-sextics and their periods

2006-05-03

arxiv.org/abs/math/0605085v1

Mathematics

Algebraic Geometry

31 pages

Scientific paper

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 H^2(X^{\vee}) from that on H^2(X); it turns out that they are isomorphic over the rationals but not over the integers (in general).

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