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 $P^{(DN)}\subseteq P^N$ 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.

10 pages, down from 12 pages in Version 1. Author info corrected. Substantial overhaul of all sections of the paper for efficient and clear exposition: significant improvements to the generality of select results; in particular, several results have been replaced or otherwise removed. Content of Sections 3 and 4 re-distributed and re-written. Segre-Veronese algebra computation added

References in corpus (4)

• A note on the cactus rank for Segre-Veronese varieties
• Uniform Harbourne-Huneke Bounds via Flat Extensions
• Symbolic powers of ideals
• Uniform Symbolic Topologies via Multinomial Expansions

Cited by in corpus (2)

• The Uniform Symbolic Topology Property for Diagonally $F$-regular Algebras
• Diagonal F-splitting and Symbolic Powers of Ideals