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Groebner bases via linkage

Gorla, Elisa and Migliore, Juan and Nagel, Uwe. (2013) Groebner bases via linkage. Journal of algebra, 384. pp. 110-134.

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Official URL: http://edoc.unibas.ch/dok/A6001404

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Abstract

In this paper, we give a sufficient condition for a set G of polynomials to be a Groebner basis with respect to a given term-order for the ideal I that it generates. Our criterion depends on the linkage pattern of the ideal I and of the ideal generated by the initial terms of the elements of G. We then apply this criterion to ideals generated by minors and pfaffians. More precisely, we consider large families of ideals generated by minors or pfaffians in a matrix or a ladder, where the size of the minors or pfaffians is allowed to vary in different regions of the matrix or the ladder. We use the sufficient condition that we established to prove that the minors or pfaffians form a reduced Groebner basis for the ideal that they generate, with respect to any diagonal or anti-diagonal term-order. We also show that the corresponding initial ideal is Cohen-Macaulay. Our proof relies on known results in liaison theory, combined with a simple Hilbert function computation. In particular, our arguments are completely algebraic.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Algebra (Gorla)
UniBasel Contributors:Gorla, Elisa
Item Type:Article, refereed
Article Subtype:Research Article
Bibsysno:Link to catalogue
Publisher:Academic Press
ISSN:0021-8693
Note:Publication type according to Uni Basel Research Database: Journal article
Identification Number:
Last Modified:21 Jun 2018 14:50
Deposited On:21 Jun 2013 12:27

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