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On the Gorenstein property of the diagonals of the Rees algebra. (Dedicated to the memory of Fernando Serrano.)
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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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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: 19 of August of 2026]. Available at: https://hdl.handle.net/2445/16932