Factorial algebraic group actions and categorical quotients

JOURNAL OF ALGEBRA

卷:387

Article

Arzhantsev, Ivan V.^1,2  Celik, Devrim³  Hausen, Juergen³ 

[1] Moscow MV Lomonosov State Univ, Fac Mech & Math, Dept Higher Algebra, Moscow 119991, Russia

[2] Natl Res Univ, Higher Sch Econ, Moscow 109028, Russia

[3] Univ Tubingen, Math Inst, D-72076 Tubingen, Germany

关键词: Algebraic variety;    Algebraic group;    Unipotent group;    Action;    Categorical quotient;    Constructible set;    Geometric Invariant Theory;    Cox ring;   

DOI  :  10.1016/j.jalgebra.2013.04.018

来源: Elsevier

【 摘 要 】

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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free