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

Aguirre, Edith; Jarrah, Abdul Salam; Laubenbacher, Reinhard; Ortiz-Navarro, Juan Ariel; Torrez, Rogelio

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

Authors

Aguirre, Edith

Jarrah, Abdul Salam

Laubenbacher, Reinhard

Ortiz-Navarro, Juan Ariel

Torrez, Rogelio

Description

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 $n=2$.
6 pages, 1 figure