Francesco Bisio

Università degli Studi di Genova

A level initial ideal of the 2-minors determinantal ideal

For $K$ a field, let $X$ be a $m\times n$ matrix of variables over $K$ and $S=K[X]$. We consider the determinantal ideal $J$ of $S$ generated by the $2$-minors of $X$. We find a suitable monomial order over $S$ such that $I$, the initial ideal of $J$ with respect to that order, is level, namely, it is Cohen-Macaulay and the socle of an Artinian reduction of the $N$-graded algebra $S/I$ is concentrated in only one degree. Moreover, we compare the Betti tables of $J$ with the tables of all its possible initial ideals.