The SpaceCurves package in Macaulay2
type: Item
instance of: scholarly article
title: The SpaceCurves package in Macaulay2
zbMATH Open document ID: 1408.14004
author: Mengyuan Zhang
published in: The Journal of Software for Algebra and Geometry
publication date: 2019-01-08T00:00:00Z
review text: The Macaulay2 package under review, called SpaceCurves.m2, is a new tool, which generates curves in the projective three-space. The author introduces this package, devoted to three types of curves: smooth curves, arithmetical Cohen-Macaulay (ACM) curves, and minimal curves in a given even liaison class. The case of smooth curves is discussed exhausting all possibilities of pairs. Three types of curves are approached in this case: curves on a smooth quadric surface, curves on a smooth cubic surface, and curves on a rational quartic surface. The case of ACM curves in the projective three-space is presented by illustrating the stratification of Hilbert schemes of ACM curves by Betti tables. The case of curve that is minimal in a given even liaison class uses the even liaison class specified in two manners: either by the ideal of a curve in the even liaison class, or by a finite length module. Many illustrating examples are included.
reviewed by: Gabriela Cristescu
Mathematics Subject Classification ID: 14-04
Mathematics Subject Classification ID: 14H50
Mathematics Subject Classification ID: 14Hxx
Mathematics Subject Classification ID: 14M06
zbMATH DE Number: 6998251
zbMATH Keywords: space curves
zbMATH Keywords: minimal curves
zbMATH Keywords: Rao module
zbMATH Keywords: liaison theory
zbMATH Keywords: ACM curves
zbMATH Keywords: smooth curves
describes a project that uses: Macaulay2
MaRDI profile type: Publication
full work available at URL: jsag.2018.8.31
OpenAlex ID: W2810068066
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cites work: An algorithm for computing minimal curves
cites work: Q4143433
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cites work: Liaison among curves in \(\mathbb{P}^3\)
Wikidata QID: Q129598319
DOI: 10.2140/JSAG.2018.8.31
description: scientific article; zbMATH DE number 6998251