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

Research paper by Olga Lavila-Vidal

Indexed on: 01 Dec '98Published on: 01 Dec '98Published in: Manuscripta Mathematica

#### Abstract

We consider the blowing up of ℙk/n−1 along a closed subscheme defined by a homogeneous idealI ∪A=k[X1, …,Xn] generated by forms of degree ≤d, and its projective embeddings by the linear systems corresponding to (Ie)c, forc≥de+1. The homogeneous coordinate rings of these embeddings arek[(Ie)c]. One wants to study the Cohen-Macaulay property of these rings. We will prove that if the Rees algebraRA(I) is Cohen-Macaulay, thenk[(Ie)c] are Cohen-Macaulay forc>>e>0, thus proving a conjecture stated by A. Conca, J. Herzog, N.V. Trung and G. Valla.