Stable reductive varieties I: Affine varieties

摘要

The main motivation for this work is to extend the construction of the moduli spaces of polarized abelian varieties A_g and their compactifications to a non-commutative setting. Recall that A_g admits many natural compactifi-cations: toroidal (due to Mumford et al.), Satake-Baily-Borel, Borel-Serre etc. Of these, one special toroidal compactification has an interpretation as the moduli space of projective stable pairs (X, D): see [Ale02], which extends the much earlier work of Namikawa [Nam76]. The former paper also constructs the moduli space of stable pairs with torus action, and semiabelian action.