Algebraic Geometry Seminar
Orsola Tommasi
Hannover
Stable cohomology of toroidal compactifications of the moduli space of abelian varieties
Abstract: It is well known that the cohomology of the moduli space A_g of
g-dimensional principally polarized abelian varieties stabilizes when
the degree is smaller than g. This is a classical result of Borel on the
stable cohomology of the symplectic group. By work of Charney and Lee,
also the stable cohomology of the minimal compactification of Ag, the
Satake compactification, is explicitly known.
In this talk, we consider the stable cohomology of toroidal
compactifications of A_g, concentrating on the perfect cone
compactification and the matroidal partial compactification. We prove
stability results for these compactifications and show that all stable
cohomology is algebraic. This is joint work with S. Grushevsky and K.
Hulek.
Wednesday October 16, 2013 at 4:00 PM in SEO 427