Fuxiang Yang

University of Notre Dame

Syzygies of linearly presented ideals

We let $S$ be the polynomial ring over the complex numbers, $\mathfrak{m}$ be the maximal ideal, and $I$ be an $\mathfrak{m}$-primary linearly presented homogeneous ideal generated in degree $d$. We proved a sharp lower bound on the number of minimal generators of $I$, we obtained an effective lower bound on the powers $t$ such that $I^t$ coincide with a power of the maximal ideal $\mathfrak{m}$, and we proved a sharp lower bound on the Castelnuovo-Mumford regularity of $I$.