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TitleGröbner bases for spaces of quadrics of low codimension
Author(s) Aldo Conca
TypeArticle in Journal
AbstractLet R = oplusi ge 0 Ri be a quadratic standard graded K-algebra. Backelin has shown that R is Koszul provided dim R2 le 2. One may wonder whether, under the same assumption, R is defined by a Gröbner basis of quadrics. In other words, one may ask whether an ideal I in a polynomial ring S generated by a space of quadrics of codimension le 2 always has a Gröbner basis of quadrics. We will prove that this is indeed the case with, essentially, one exception given by the ideal I = (x2, xy, y2 - xz, yz) sub K[x, y, z]. We show also that if R is a generic quadratic algebra with dim R2 < dim R1 then R is defined by a Gröbner basis of quadrics.
Length14
ISSN0196-8858
CopyrightAcademic Press
File
URL dx.doi.org/10.1006/aama.1999.0676
LanguageEnglish
JournalAdvances in Applied Mathematics
Volume24
Number2
Pages111-124
PublisherAcademic Press, Inc.
AddressOrlando, FL, USA
Year2000
MonthFebruary
Translation No
Refereed No
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