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arXiv · 2610.30057

Differential powers of monomial ideals in affine semigroup rings

Soumyadeep Misra·Christopher Wong
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Abstract

This article gives explicit descriptions for differential powers of monomial ideals in certain (possibly non-normal) affine semigroup rings. We use these descriptions to show that the topologies defined by the ordinary, symbolic, and differential powers of any monomial ideal are all linearly equivalent. We then prove the existence of differential signature in our settings, relating it to the volume of some convex polytope. Finally, we apply our results to pinched Veronese rings.

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Soumyadeep Misra, Christopher Wong. 2026-10-21. Differential powers of monomial ideals in affine semigroup rings. https://arxiv.org/abs/2610.30057

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