On lower bounds for the F-pure threshold of equigenerated ideals

Abstract

Let $k$ be a field of positive characteristic and $R = k[x_0,\dots, x_n]$. We consider ideals $I\subseteq R$ generated by homogeneous polynomials of degree $d$. Takagi and Watanabe proved that $\mathrm{fpt}(I)\geq \mathrm{height}(I)/d$; we classify ideals $I$ for which equality is attained. Inspired by a result of de Fernex, Ein, and Musta\c{t}\u{a}, we give a lower bound on $\mathrm{fpt}(I)$ in terms of the height of $\tau(I^{\mathrm{fpt}(I)})$.