engleski

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

We present an algorithm for explicitly computing the number of generators of the stable cohomology algebra of any rationally smooth partial toroidal compactification of $\ab$ 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 Matr, in terms of matroids that are irreducible with respect to the 1-sum 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 Perf. This suggests the existence of an algebra structure on the cohomology of the perfect toroidal compactification.

Toroidal compactification ; Moduli Spaces ; Polyhedral Complex

Appendix by Mathieu Dutour Sikiric