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Degrevlex Gröbner bases of generic complete intersections

✍ Scribed by Guillermo Moreno-Socı́as

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
246 KB
Volume
180
Category
Article
ISSN
0022-4049

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✦ Synopsis

In this paper, we study the Hilbert-Samuel function of a generic standard graded K-algebra K[X1; : : : ; Xn]=(g1; : : : ; gm) when reÿned by an (')-adic ÿltration, ' being a linear form. From this we obtain a structure theorem which describes the stairs of a generic complete intersection for the degree-reverse-lexicographic order. We show what this means for generic standard (or Gr obner) bases for this order; in particular, we consider an "orderly ÿlling up" conjecture, and we propose a strategy for the standard basis algorithm which could be useful in generic-like cases.

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