Iterative Nash blowups resolve singularities in normal toric surfaces with defined minimal generating sets.
We show that iterating Nash blowups resolves the singularities of normal toric surfaces satisfying the following property: the minimal generating set of the corresponding semigroup is contained in one or two segments. We also provide examples with an arbitrary number of segments for which the same result holds.
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Duarte et al. (2025) studied this question.
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