Cohomology of the Second Voronoi Compactification of mathcal A_4

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

2010 Mathematics Subject Classification: Primary 14K10; Secondary 14F25, 14C15, 14D22

Keywords and Phrases: Abelian varieties, Voronoi compactification, perfect cone compactification, Chow ring, cohomology ring

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