Factorization of anticanonical maps of Fano type varieties

Abstract

The purpose of the present paper is to generalize Sakai's work on anticanonical models of rational surfaces to varieties of Fano type. We rst prove a characterization of Fano type varieties using the singularities of anti- canonical models. Secondly, we study the decomposition of the anticanonical map using the KX-minimal model program.