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Differential powers of monomial ideals in affine semigroup rings
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.
Related
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BibTeX
@misc{misra2026differential,
title = {{Differential powers of monomial ideals in affine semigroup rings}},
author = {Soumyadeep Misra and Christopher Wong},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30057},
eprint = {2610.30057},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30057},
}
RIS
TY - UNPB
TI - Differential powers of monomial ideals in affine semigroup rings
AU - Soumyadeep Misra
AU - Christopher Wong
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30057
UR - https://arxiv.org/abs/2610.30057
AB - 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.
ER -