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1998

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/16932

On the Gorenstein property of the diagonals of the Rees algebra. (Dedicated to the memory of Fernando Serrano.)

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Abstract

Let Y be a closed subscheme of Pn−1 k defined by a homogeneous ideal I⊂ A=k[X1,...,Xn], and X obtained by blowing up Pn−1 k along Y. Denote by Ic the degree c part of I and assume that I is generated by forms of degree ≤ d. Then the rings k[(Ie)c] are coordinate rings of projective embeddings of X in PN−1 k , where N=dimk(Ie)c for c ≥ de+1. The aim of this paper is to study the Gorenstein property of the rings k[(Ie)c] . Under mild hypothesis we prove that there exist at most a finite number of diagonals (c, e) such that k[(Ie)c] is Gorenstein, and we determine them for several families of ideals.

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Anells commutatius, Geometria algebraica, Categories (Matemàtica)

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Commutative rings, Algebraic geometry, Categories (Mathematics)

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LAVILA VIDAL, Olga and ZARZUELA, Santiago. On the Gorenstein property of the diagonals of the Rees algebra. (Dedicated to the memory of Fernando Serrano.). Collectanea Mathematica. 1998. Vol. 49, num. 2-3, pags. 383-397. ISSN 0010-0757. [consulted: 18 of June of 2026]. Available at: https://hdl.handle.net/2445/16932

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