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.
DFG Programme
CRC/Transregios
