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24 April 2024
 
  » arxiv » 0711.4740

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On the depth of invariant rings of infinite groups
Martin Kohls ;
Date 29 Nov 2007
AbstractLet 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.
Source arXiv, 0711.4740
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