Groebner bases for spaces of quadrics of codimension 3

Details Groebner bases for spaces of quadrics of codimension 3 Groebner bases for spaces of quadrics of codimension 3

2007-09-25

arxiv.org/abs/0709.3917v2

Mathematics

Commutative Algebra

Minor changes, to appear in the J. Pure Applied Algebra

Scientific paper

Let $R=\oplus_{i\geq 0} R_i$ be an Artinian standard graded $K$-algebra defined by quadrics. Assume that $\dim R_2\leq 3$ and that $K$ is algebraically closed of characteristic $\neq 2$. We show that $R$ is defined by a Gr\"obner basis of quadrics with, essentially, one exception. The exception is given by $K[x,y,z]/I$ where $I$ is a complete intersection of 3 quadrics not containing the square of a linear form.

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