Integral cohomology of the generalized Kummer fourfold

Author(s)

Kapfer, Simon ^[1] ; Menet, Gregoire ^{[2, 3]}

Affiliation

^[1] Augsburg Univ, Inst Math, D-86159 Augsburg - Germany

^[2] Univ Estadual Campinas, Inst Matemat Estat & Camputacao Cient, Cx Postal 6065, BR-13083970 Campinas, SP - Brazil

^[3] Univ Burgundy, IMB, 9 Ave Alain Savary, F-21000 Dijon - France

• Document type: Journal article
• Source: ALGEBRAIC GEOMETRY; v. 5, n. 5, p. 523-567, SEP 2018.
• Web of Science Citations: 0

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. (AU)

• FAPESP's process: 14/05733-9 - Geometry of irreducible symplectic varieties
• Grantee: Grégoire Menet
• Support Opportunities: Scholarships in Brazil - Post-Doctoral