Constructing schemes with prescribed cohomology in arbitrary codimension
type: Item
instance of: scholarly article
title: Constructing schemes with prescribed cohomology in arbitrary codimension
zbMATH Open document ID: 0979.13018
DOI: 10.1016/S0022-4049(99)00136-X
author: Uwe Nagel
author: Chris Peterson
author: Juan C. Migliore
published in: Journal of Pure and Applied Algebra
publication date: 2000-11-21T00:00:00Z
review text: Let \(k\) be a field, \(R = k[X_1, \dots, X_n]\) a polynomial ring, \(\mathfrak m = (X_1, \dots, X_n)\) and \(M_2\), \dots, \(M_{d-1}\) graded \(R\)-modules of finite length where \(2 < d \leq n-2\). The authors give a homogeneous ideal \(I\) of \(R\) such that \(\dim R/I = d\) and H\(_{\mathfrak m}^i(R/I) \cong M_i\) (up to shift) for \(2 \leq i \leq d-1\). If \(n-d = 2\), then Evans and Griffith already gave such a ring by using Bourbaki sequence. However the authors use the theory of orientable modules and give the ring when \(n - d \geq 3\).
reviewed by: Takesi Kawasaki
Mathematics Subject Classification ID: 13D45
Mathematics Subject Classification ID: 14B15
Mathematics Subject Classification ID: 13D02
Mathematics Subject Classification ID: 14F99
Mathematics Subject Classification ID: 14J60
Mathematics Subject Classification ID: 14A10
zbMATH DE Number: 1517304
zbMATH Keywords: local cohomology
zbMATH Keywords: prescribed cohomology
zbMATH Keywords: graded modules
zbMATH Keywords: orientable modules
describes a project that uses: Macaulay2
describes a project that uses: CoCoA
MaRDI profile type: Publication
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Wikidata QID: Q126339951
description: scientific article; zbMATH DE number 1517304