Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4585149 | Journal of Algebra | 2013 | 12 Pages |
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 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Ivan V. Arzhantsev, Devrim Celik, Jürgen Hausen,