Factorial algebraic group actions and categorical quotients - Mathematics > Algebraic GeometryReport as inadecuate




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Abstract: Given an action of an affine algebraic group with only trivial characters ona factorial variety, we ask for categorical quotients. We characterizeexistence in the category of algebraic varieties. Moreover, allowingconstructible sets as quotients, we obtain a more general existence resultwhich, for example, settles the case of a finitely generated algebra ofinvariants. As an application, we provide a combinatorial GIT-type constructionof categorial quotients for actions on, e.g. complete varieties with finitelygenerated Cox ring via lifting to the characteristic space.



Author: I.V. Arzhantsev, D. Celik, J. Hausen

Source: https://arxiv.org/



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