Abundance for slc surfaces over arbitrary fields

Abstract

We prove the abundance conjecture for projective slc surfaces over arbitrary fields of positive characteristic. The proof relies on abundance for lc surfaces over abritrary fields, proved by Tanaka, and on the technique of Hacon and Xu to descend semi-ampleness from the normalization. We also present applications to dlt threefold pairs, and to mixed characteristic families of surfaces.

Keywords

• mathematics - algebraic geometry