On the Gorenstein property of the diagonals of the Rees algebra

• Autores: Santiago Zarzuela , Olga Lavila Vidal
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 49, Fasc. 2-3, 1998, págs. 383-398
• Idioma: inglés
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• Resumen

  • Let $Y$ be a closed subscheme of $\mathbb{P}^{n-1}_k$ defined by a homogeneous ideal $I\subset A=k[X1,\cdots,Xn]$, and $X$ obtained by blowing up $\mathbb{P}^{n-1}_k$ along $Y$. Denote by $I_c$ the degree $c$ part of $I$ and assume that $I$ is generated by forms of degree $\leq d$. Then the rings $k[(I^e)_c]$ are coordinate rings of projective embeddings of $X$ in $\mathbb{P}^{N-1}_k$ , where $N=dim_k(I^e)_c$ for $c\geq de+1$. The aim of this paper is to study the Gorenstein property of the rings $k[(I^e)_c]$ . Under mild hypothesis we prove that there exist at most a finite number of diagonals ($c, e$) such that $k[(I^e)_c]$ is Gorenstein, and we determine them for several families of ideals.