Factorization of anticanonical maps of Fano type varieties

TL;DR

This paper generalizes Sakai's work on anticanonical models from rational surfaces to Fano type varieties, characterizing these varieties via their anticanonical models and analyzing their anticanonical maps through the minimal model program.

Contribution

It introduces a new characterization of Fano type varieties based on anticanonical model singularities and studies the decomposition of their anticanonical maps.

Findings

Characterization of Fano type varieties using anticanonical model singularities

Decomposition of anticanonical maps via the minimal model program

Extension of Sakai's results from rational surfaces to higher-dimensional 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.