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 first prove a characterization of Fano type varieties using the singularities of anticanonical models. Secondly, we study the decomposition of the anticanonical map using the $K_X$-minimal model program.

19 pages. We have corrected typos and mistakes. This will appear in IMRN

References in corpus (2)

• Introduction to the log minimal model program for log canonical pairs
• Redundant blow-ups of rational surfaces with big anticanonical divisor