Project B7: Chow groups and compactifications of moduli spaces

In algebraic geometry, moduli spaces are geometric spaces (usually schemes or stacks), whose points represent algebro-geometric objects of a fixed kind. The present project studies geometric and arithmetic aspects of moduli spaces allowing toroidal compactifications. For this, we will consider intersection theoretic and combinatorial properties of so called Weil and Cartier b-Chow groups. One main goal is an infinite Chern--Weil theory for singular, semipositive, invariant metrics on automorphic vector bundles on mixed Shimura varieties.