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Regular version of the site

Article

Factorial algebraic group actions and categorical quotients

Journal of Algebra. 2013. Vol. 387. P. 87-98.
Arzhantsev I., Celik D., Hausen J.

Given an action of an affine algebraic group with only trivial characters on a factorial variety, we ask for categorical quotients. We characterize existence in the category of algebraic varieties. Moreover, allowing constructible sets as quotients, we obtain a more general existence result, which, for example, settles the case of afinitely generated algebra of invariants. As an application, we provide a combinatorial GIT-type construction of categorical quotients for actions of not necessarily reductive groups on, e.g. complete varieties with finitely generated Cox ring via lifting to the characteristic space