On the equations which are needed to define a closed subscheme of the projective space
type: Item
instance of: scholarly article
title: On the equations which are needed to define a closed subscheme of the projective space
zbMATH Open document ID: 0833.14001
DOI: 10.1016/0022-4049(95)90025-X
author: Dario Portelli
author: Walter Spangher
published in: Journal of Pure and Applied Algebra
publication date: 1995-04-11T00:00:00Z
review text: Let \(R = k[X_0, \ldots, X_n]\) be the polynomial algebra in \(n + 1\) variables over an infinite field \(k\), and let \(I\) be a proper homogeneous ideal of \(R\). The main result of this paper shows that there exists a minimal system of homogeneous generators \(g_1, \ldots, g_s\) of \(I\) such that \(g_1, \ldots, g_t\) define the subscheme \(X = \text{Proj} (R/I)\) of \(\mathbb{P}^n_k\) scheme-theoretically, where the integer \(t\) \((t \leq s)\) is the minimal number of homogeneous equations needed to define \(X\) scheme-theoretically in \(\mathbb{P}^n_k\).
reviewed by: Lucian Bădescu
Mathematics Subject Classification ID: 14A15
Mathematics Subject Classification ID: 14M10
Mathematics Subject Classification ID: 14N05
zbMATH DE Number: 737483
zbMATH Keywords: equations defining a subscheme
zbMATH Keywords: polynomial algebra
zbMATH Keywords: minimal system of homogeneous generators
MaRDI profile type: Publication
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full work available at URL: 0022-4049(95)90025-x
OpenAlex ID: W2064011527
description: scientific article; zbMATH DE number 737483