Double covers of quadratic degeneracy and Lagrangian intersection loci
Abstract
We explain a general construction of double covers of quadratic degeneracy loci and Lagrangian intersection loci based on reflexive sheaves. We relate the double covers of quadratic degeneracy loci to the Stein factorizations of the relative Hilbert schemes of linear spaces of the corresponding quadric fibrations. We give a criterion for these double covers to be nonsingular. As applications of these results, we show that the double covers of the EPW sextics obtained by our construction give O'Grady's double EPW sextics and that an analogous construction gives Iliev-Kapustka-Kapustka-Ranestad's EPW cubes.
Keywords
Cite
@article{arxiv.1803.00799,
title = {Double covers of quadratic degeneracy and Lagrangian intersection loci},
author = {Olivier Debarre and Alexander Kuznetsov},
journal= {arXiv preprint arXiv:1803.00799},
year = {2019}
}
Comments
26 pages. As suggested by Nick Addington, we added an application to double covers of symmetroids. This third version also includes simple but useful additions in Theorem 5.2(2) and 5.7(2), and new Lemmas 3.3 and 4.3