Generic ideals and Moreno-Soc{\'ı}as conjecture

Details Generic ideals and Moreno-Soc{\'ı}as conjecture Generic ideals and Moreno-Soc{\'ı}as conjecture

2001-04-04

arxiv.org/abs/math/0104047v1

Mathematics

Commutative Algebra

6 pages, 1 figure

Scientific paper

Let $f_1, ..., f_n$ be homogeneous polynomials generating a generic ideal $I$ in the ring of polynomials in $n$ variables over an infinite field. Moreno-Soc\'ias conjectured that for the graded reverse lexicographic term ordering, the initial ideal ${\rm in}(I)$ is a weakly reverse lexicographic ideal. This paper contains a new proof of Moreno-Soc{\'\i}as' conjecture for the case $n=2$.

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