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## Andrew Dancer, Jørgen Ellegaard Andersen, and Oscar García-Prada

Print publication date: 2018

Print ISBN-13: 9780198802020

Published to Oxford Scholarship Online: December 2018

DOI: 10.1093/oso/9780198802020.001.0001

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# Stable Betti Numbers of (Partial) Toroidal Compactifications of the Moduli Space of Abelian Varieties

Chapter:
(p.581) 24 Stable Betti Numbers of (Partial) Toroidal Compactifications of the Moduli Space of Abelian Varieties
Source:
Geometry and Physics: Volume II
Publisher:
Oxford University Press
DOI:10.1093/oso/9780198802020.003.0024

This chapter presents an algorithm for explicitly computing the number of generators of the stable cohomology algebra of any rationally smooth partial toroidal compactification of Ag, satisfying certain additivity and finiteness properties, in terms of the combinatorics of the corresponding toric fans. In particular, the algorithm determines the stable cohomology of the matroidal partial compactification, in terms of simple regular matroids that are irreducible with respect to the 1-sum operation, and their automorphism groups. The algorithm also applies to compute the stable Betti numbers in close to top degree for the perfect cone toroidal compactification. This suggests the existence of an algebra structure on the stable cohomology of the perfect cone compactification in close to top degree.

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