EVENT DETAILS AND ABSTRACT

Title: Fuchsian subgroups and Albanese varieties of arithmetic quotients of SU(2, 1) / U(2).
Speaker: Matthew Stover
Speaker Info: Michigan
Brief Description:
Special Note:
Abstract:

I will describe joint work with Ted Chinburg on applying weak Lefschetz-type theorems to collections of holomorphically embedded totally geodesic subspaces of smooth compact arithmetic quotients of SU(2, 1) / U(2), i.e., embeddings coming from the natural maps U(1, 1) \to SU(2, 1). For those smooth compact arithmetic quotients arising from hermitian forms over CM fields, this allows us to prove that the Albanese variety of the associated projective algebraic surface is built from Jacobians of holomorphically embedded totally geodesic submanifolds, that is, quotients of the hyperbolic plane by cocompact arithmetic Fuchsian groups. I will also touch on the relationship between our results and a theorem of Murty and Ramakrishnan on the structure of the Albanese variety when the lattice is a neat congruence subgroup and discuss how a higher-dimensional version of our results would resolve some open problems on the structure of the cohomology of arithmetic subgroups of SU(n, 1) arising from hermitian forms over central simple algebras with involution of second kind.