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TitleDeformations of border bases.
Author(s) Martin Kreuzer, Lorenzo Robbiano
TypeArticle in Journal
AbstractBorder bases have recently attracted a lot of attention. Here we study the problem of generalizing one of the main tools of Gröbner basis theory, namely the flat deformation to the leading term ideal, to the border basis setting. After showing that the straightforward approach based on the deformation to the degree form idealworks only under additional hypotheses, we introduce border basis schemes and universal border basis families. With their help the problem can be rephrased as the search for a certain rational curve on a border basis scheme. We construct the system of generators of the vanishing ideal of the border basis scheme in different ways and study the question of how to minimalize it. For homogeneous ideals, we also introduce a homogeneous border basis scheme and prove that it is an affine space in certain cases. In these cases it is then easy to write down the desired deformations explicitly.
KeywordsBorder basis, Gröbner basis, deformation
ISSN0010-0757; 2038-4815/e
URL http://link.springer.com/article/10.1007%2FBF03191188
LanguageEnglish
JournalCollect. Math.
Volume59
Number3
Pages275--297
PublisherSpringer, Milan; Universitat de Barcelona, Institut de Matem`atica, Barcelona
Year2008
Edition0
Translation No
Refereed No
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