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## The automorphism group of a variety with torus action of complexity one

Moscow Mathematical Journal. 2014. Vol. 14. No. 3. P. 429-471.
Arzhantsev I., Hausen J., Herppich E., Liendo A.

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.