Details:
Title  Gröbner bases for spaces of quadrics of low codimension  Author(s)  Aldo Conca  Type  Article in Journal  Abstract  Let R = oplusi ge 0 Ri be a quadratic standard graded Kalgebra. 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.  Length  14  ISSN  01968858  Copyright  Academic Press 
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 URL 
dx.doi.org/10.1006/aama.1999.0676 
Language  English  Journal  Advances in Applied Mathematics  Volume  24  Number  2  Pages  111124  Publisher  Academic Press, Inc.  Address  Orlando, FL, USA  Year  2000  Month  February  Translation 
No  Refereed 
No 
