Factorization of Anticanonical Maps of Fano Type Variety

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 first prove a characterization of Fano Type Variety using the singularities of anticanonical models. Secondly, we study the decomposition of the anticanonical map using the K-X-minimal model program.