Divisorial models of normal varieties

TL;DR

This paper proves finite generation of the canonical ring for certain varieties, introduces a nefness concept for non-Q-Gorenstein varieties, and explores these properties in the context of toric varieties.

Contribution

It establishes finite generation results for canonical rings and introduces a new nefness notion for non-Q-Gorenstein varieties, expanding the understanding of their structure.

Findings

Canonical ring of a canonical variety is finitely generated.

Canonical varieties are klt iff R(-K_X) is finitely generated.

Nefness for non-Q-Gorenstein varieties has useful properties.

Abstract

We prove that the canonical ring of a canonical variety in the sense of de Fernex and Hacon is finitely generated. We prove that canonical varieties are klt if and only if R(-K_X) is finitely generated. We introduce a notion of nefness for non-Q-Gorenstein varieties and study some of its properties. We then focus on these properties for non-Q-Gorenstein toric varieties.