Applications of some properties of the canonical module in computational projective algebraic geometry
type: Item
instance of: scholarly article
title: Applications of some properties of the canonical module in computational projective algebraic geometry
zbMATH Open document ID: 0982.14034
author: Marc Chardin
published in: Journal of Symbolic Computation
publication date: 2001-09-12T00:00:00Z
review text: The author uses some properties of the canonical module of an algebra for computational applications. He claims that, although no improvement on the complexities of the problems addressed is made, this approach is promising because of the simplicity of the algorithms. He also states that the complexities are essentially controlled by the complexity of the output. He first states some needed classical results on the canonical module. The first application is a way to compute the dimension of a projective scheme from generators of the defining ideal. A method to compute the Hilbert polynomial of some Cohen-Macaulay schemes is shown afterwards. In another section, a new method to describe set-theoretically the top dimensional part of a scheme is given. Finally, the author gives some regularity bounds in low dimension using liaison. The results of this paper are extended in a forthcoming joint work [\textit{M. Chardin} and \textit{B. Ulrich}, ``Liaison and Castelnuovo-Mumford regularity'', Am. J. Math. (to appear)] and can be found in \url{http://www.math.jussieu.fr/~chardin/publications.html}.
reviewed by: Juan Sabia
Mathematics Subject Classification ID: 14Q99
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 13D40
Mathematics Subject Classification ID: 13P10
zbMATH DE Number: 1471045
zbMATH Keywords: algorithms
zbMATH Keywords: canonical module
zbMATH Keywords: Hilbert polynomial
zbMATH Keywords: Cohen-Macaulay schemes
zbMATH Keywords: liaison
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1471045