Edith Aguirre

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

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 ${\rm in}(I)$ is a weakly reverse lexicographic ideal. This paper contains a new proof of Moreno-Soc{\'ı}as' conjecture for the case $n=2$.