Symbolic Powers of Toric Ideals

TL;DR

This paper explores the structure of symbolic powers of toric ideals, providing new descriptions, expressing them as saturations of regular powers, and offering computational methods for their calculation.

Contribution

It introduces a novel description of symbolic powers of toric ideals via linear maps and relates them to saturations of regular powers, enhancing computational approaches.

Findings

Symbolic powers characterized via kernel of linear maps

Symbolic powers expressed as saturations of regular powers

Provides a computational method for symbolic powers

Abstract

This paper investigates the symbolic powers of toric ideals. We first describe them in terms of the kernel of certain linear maps derived from the lattice structure of the toric ideal. Furthermore, we apply our results to show that symbolic powers of a toric ideal can also be expressed as saturations of regular powers with the monomial given by the product of all the variables. Finally, we conclude with a computationally significant result for computing symbolic powers of toric ideals.