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

Abstract

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-Socías conjectured that for the graded reverse lexicographic term ordering, the initial ideal $\mathrm{in}(I)$ is a weakly reverse lexicographic ideal. This paper contains a new proof of Moreno-Soc{\'ı}as' conjecture for the case $n=2$.

6 pages, 1 figure