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manuscripta mathematica

, Volume 95, Issue 1, pp 47–58 | Cite as

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

  • Olga Lavila-Vidal
Article

Abstract

We consider the blowing up of ℙ k /n−1 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.

Keywords

Exact Sequence Local Ring Polynomial Ring Noetherian Ring Closed Subscheme 
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Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Olga Lavila-Vidal
    • 1
  1. 1.Departament d’Àlgebra i GeometriaUniversitat de BarcelonaBarcelona, Catalunya

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