On the depth of invariant rings of infinite groups

JOURNAL OF ALGEBRA

卷:322

Article

Kohls, Martin

关键词: Invariant theory;    Vector invariants;    Cohen-Macaulay;    Depth;    Reductive groups;    First cohomology;   

DOI  :  10.1016/j.jalgebra.2009.01.019

来源: Elsevier

【 摘 要 】

Let K be an algebraically closed field. For a finitely generated graded commutative K-algebra R, let cmdef R := dim R - depth R denote the Cohen-Macaulay defect of R. Let G be a linear algebraic group over K that is reductive but not linearly reductive. We show that there exists a faithful rational representation V of G (which we will give explicitly) such that cmdef K |V-circle plus k|(G) >= k - 2 for all k is an element of N (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free