On the spectrum of certain subschemes of \(\mathbb{P}^N\)
type: Item
instance of: scholarly article
title: On the spectrum of certain subschemes of \(\mathbb{P}^N\)
zbMATH Open document ID: 0926.14026
DOI: 10.1016/S0022-4049(98)00044-9
author: Enrico Schlesinger
published in: Journal of Pure and Applied Algebra
publication date: 1999-08-23T00:00:00Z
review text: In projective geometry usually one considers graded algebras generated by elements of degree 1. Here the author considers a natural case in which more general objects occur (e.g. \(\bigoplus_{n\geq 0}H^0(C, {\mathcal O}_C(1))\) with \(C\) a locally Cohen-Macaulay even unreduced curve or, more generally, a quasi \(ACM\) subscheme \(\mathbb{P}^N)\) and studies subschemes of \(\mathbb{P}^N\) (in arbitrary characteristic) whwhich correspond to equi-dimensional Cohen-Macaulay algebras, \(A\), such that \(A\) modulo the subalgebra generated by the elements of degree 1 has finite length. The author studies the spectrum of these algebras following the theory of the spectrum for torsion free sheaves of \(\mathbb{P}^N\) previously introduced by himself. The results concern the \(h\)-vector of the algebra \(A\) in terms of the index of speciality and the number of generators in each degree of the Rao module of \(C\).
reviewed by: E. Ballico
Mathematics Subject Classification ID: 14M05
Mathematics Subject Classification ID: 13C14
Mathematics Subject Classification ID: 14N05
Mathematics Subject Classification ID: 14A05
zbMATH DE Number: 1308322
zbMATH Keywords: Cohen-Macaulay curve
zbMATH Keywords: Cohen-Macaulay algebras
zbMATH Keywords: index of speciality
zbMATH Keywords: number of generators
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1308322