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. These results are an extension of O’Grady’s construction of double covers of EPW sextics and provide an alternate construction of Iliev–Kapustka–Kapustka–Ranestad’s EPW cubes.
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Communicated by Ngaiming Mok.
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Alexander Kuznetsov was partially supported by the HSE University Basic Research Program, Russian Academic Excellence Project “5–100” and by the Program of the Presidium of the Russian Academy of Sciences 01 “Fundamental Mathematics and its Applications” under Grant PRAS-18-01.
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Debarre, O., Kuznetsov, A. Double covers of quadratic degeneracy and Lagrangian intersection loci. Math. Ann. 378, 1435–1469 (2020). https://doi.org/10.1007/s00208-019-01893-6
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DOI: https://doi.org/10.1007/s00208-019-01893-6