Mohammed Rafiq Namiq

Regularity of Symbolic Powers of Polymatroidal Ideals and Supermodular Prime Intersections

Let $S=\mathbb{K}[x_1,\ldots,x_n]$ be a polynomial ring over a field $\mathbb{K}$. For a polymatroidal ideal $I\subseteq S$ generated in degree $d$, we prove $$\omega(I^{(s)})=\operatorname{reg} I^{(s)}=\operatorname{reg} I^s=sd\qquad(s\ge1),$$ where symbolic powers use all associated primes and $\omega$ denotes the la...