This analysis reveals relationships between symbolic powers and regular powers of toric ideals, suggesting new computation methods.
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.
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Favacchio et al. (2025) studied this question.
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