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On the Cohen-Macaulay property of diagonal subalgebras of the Rees algebra

Abstract

We consider the blowing up of ℙ /n−1 k along a closed subscheme defined by a homogeneous idealIA=k[X 1, …,X n ] generated by forms of degree ≤d, and its projective embeddings by the linear systems corresponding to (I e) c , forcde+1. The homogeneous coordinate rings of these embeddings arek[(I e) c ]. One wants to study the Cohen-Macaulay property of these rings. We will prove that if the Rees algebraR A (I) is Cohen-Macaulay, thenk[(I e) c ] are Cohen-Macaulay forc>>e>0, thus proving a conjecture stated by A. Conca, J. Herzog, N.V. Trung and G. Valla.

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Supported by a F.P.I. grant of Ministerio de Educación y Ciencia (Spain)

This article was processed by the author using the LATEX style filecljour1 from Springer-Verlag.

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Lavila-Vidal, O. On the Cohen-Macaulay property of diagonal subalgebras of the Rees algebra. Manuscripta Math 95, 47–58 (1998). https://doi.org/10.1007/BF02678014

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Keywords

  • Exact Sequence
  • Local Ring
  • Polynomial Ring
  • Noetherian Ring
  • Closed Subscheme