Integral cohomology of the generalized Kummer fourfold

Abstract : We describe the integral cohomology of the generalized Kummer fourfold, giving an explicit basis, using Hilbert scheme cohomology and tools developed by Hassett and Tschinkel. Then, we apply our results to an irreducible holomorphic symplectic variety with singularities, obtained by a partial resolution of the generalized Kummer fourfold quotiented by a symplectic involution. We calculate the Beauville-Bogomolov form of this new variety, presenting the first example of such a form that is odd.
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Contributor : Imb - Université de Bourgogne <>
Submitted on : Tuesday, January 29, 2019 - 9:58:18 AM
Last modification on : Thursday, February 7, 2019 - 2:46:07 PM

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Simon Kapfer, Grégoire Menet. Integral cohomology of the generalized Kummer fourfold. Algebraic Geometry, Foundation Compositio Mathematica, 2018, 5 (5), pp.523-567. ⟨10.14231/AG-2018-014⟩. ⟨hal-01997500⟩

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