On the depth of invariant rings of infinite groups

Details On the depth of invariant rings of infinite groups On the depth of invariant rings of infinite groups

2007-11-29

arxiv.org/abs/0711.4740v3

J. Algebra 322 (2009), 210-218

Mathematics

Commutative Algebra

11 pages

Scientific paper

Let K be an algebraically closed field. For a finitely generated graded 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[\sum_i=1^k V]^G >= k-2 for all k. We give refinements in the case G = SL2.

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