Fano manifolds of degree ten and EPW sextics

Details Fano manifolds of degree ten and EPW sextics Fano manifolds of degree ten and EPW sextics

2009-07-16

arxiv.org/abs/0907.2781v1

Mathematics

Algebraic Geometry

Scientific paper

O'Grady showed that certain special sextics in $\mathbb{P}^5$ 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.

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