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Action of finite groups on Rees algebras and Gorensteinness in invariant subrings

Published online by Cambridge University Press:  20 January 2009

Shin-Ichiro Iai
Shin-Ichiro Iai
Affiliation:
Department of Mathematics School of Science and Technology, Meiji University, 214–71, Japan E-mail address: [email protected]
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Let G be a finite group of order N and assume that G acts on a Cohen-Macaulay local ring A as automorphisms of rings. Let N be a unit in A. For a given G-stable ideal I in A we denote by R(I) = ⊕n≥0In and = G(I) = ⊕n≥0In/In+1 the Rees algebra and the associated graded ring of I, respectively. Then G naturally acts on R(I) and G(I) too. In this paper the conditions under which the invariant subrings R(I)G of R(I) are Cohen-Macaulay and/or Gorenstein rings are described in connection with the corresponding ring-theoretic properties of G(I)G and the a-invariants a(G(I)G of G(I)G. Consequences and some applications are discussed.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 42 , Issue 2 , June 1999 , pp. 393 - 401
Copyright
Copyright © Edinburgh Mathematical Society 1999

References

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