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arXiv · 0908.0443

Factorial algebraic group actions and categorical quotients

I. V. Arzhantsev·D. Celik·J. Hausen
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Abstract

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 a finitely generated algebra of invariants. As an application, we provide a combinatorial GIT-type construction of categorial quotients for actions on, e.g. complete varieties with finitely generated Cox ring via lifting to the characteristic space.

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I. V. Arzhantsev, D. Celik, J. Hausen. 2009-08-04. Factorial algebraic group actions and categorical quotients. https://arxiv.org/abs/0908.0443

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