Divisorial models of normal varieties

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.

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