Cohomology of the second Voronoi compactification of $\mathcal A_4$

Klaus Hulek; Orsola Tommasi

doi:10.4171/dm/366

JournalsdmVol. 17pp. 195–244

Cohomology of the second Voronoi compactification of $A_{4}$

Klaus Hulek
Leibniz Universität Hannover Leibniz Universität Hannover Institut für Algebraische Geometrie Institut für Algebraische Geometrie Welfengarten 1 Welfengarten 1 D-30167 Hannover D-30167 Hannover Germany Germany
Orsola Tommasi
Leibniz Universität Hannover Leibniz Universität Hannover Institut für Algebraische Geometrie Institut für Algebraische Geometrie Welfengarten 1 Welfengarten 1 D-30167 Hannover D-30167 Hannover Germany Germany

$Cohomology of the second Voronoi compactification of $\mathcal A_4$ cover$

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Abstract

In this paper we compute the cohomology groups of the second Voronoi and the perfect cone compactification $A_{4}^{Vor}$ and $A_{4}^{perf}$ respectively, of the moduli space of abelian fourfolds in degree $\leq 9$ . The main tool is the investigation of the strata of $A_{4}^{Vor}$ corresponding to semi-abelic varieties with constant torus rank.

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Klaus Hulek, Orsola Tommasi, Cohomology of the second Voronoi compactification of $A_{4}$ . Doc. Math. 17 (2012), pp. 195–244

DOI 10.4171/DM/366