Book chapter, 2018

We present an algorithm for explicitly computing the number of generators of the stable cohomology algebra of any rationally smooth partial toroidal compactification ofA g 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 A Matrg , 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 APerf g. This suggests the existence of an algebra structure on H top−kstable (A Perfg , Q).

Moduli space

Toroidal compactification

Partial compactification

Betti number

Abelian varieties

Stony Brook University

University of Hanover

Chalmers, Mathematical Sciences, Algebra and geometry

Ruder Boskovic Institute

582-610

Algebra and Logic

Geometry

Mathematical Analysis

10.1093/oso/9780198802020.003.0024