Martin Olsson

A higher dimensional version of generalized elliptic curves.

Abstract: I will discuss a higher dimensional version of Deligne and Rapoport's notion of "generalized elliptic curve" and explain how one can use it to obtain canonical (arithmetic) compactifications of moduli spaces for abelian varieties with polarization (not necessarily principal) and level structure. These moduli spaces are obtained as solutions to certain moduli problems. In the case of $A_g$ (the moduli space of principally polarized abelian varieties) the compactification is equal to the normalization of the main component of Alexeev's canonical compactification of $A_g$.