Uniform Symbolic Topologies in Normal Toric Rings

Abstract

Given a normal toric algebra $R$, we compute a uniform integer $D = D(R) > 0$ such that the symbolic power $P^{(D N)} \subseteq P^N$ for all $N >0$ and all monomial primes $P$. We compute the multiplier $D$ explicitly in terms of the polyhedral cone data defining $R$. In this toric setting, we draw a connection with the F-signature of $R$ in positive characteristic.