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Analytic multiplier ideals of toric plurisubharmonic functions on a toric complex space
Abstract
In this paper, we study analytic multiplier ideal sheaves of toric plurisubharmonic functions on normal affine toric complex analytic spaces equipped with torus-invariant rational divisors, assuming that a positive integer multiple of the log canonical divisor is Cartier. We describe these sheaves in terms of Newton convex bodies and show that they are globally generated by finitely many meromorphic monomials. Our results generalize the description of An and the formulas of Howald and Blickle for monomial ideals, and recover the descriptions of Rashkovskii and Guenancia on affine space. We also extend this description to weights obtained by subtracting positive rational multiples of monomial ideal weights.
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BibTeX
@misc{seo2026analytic,
title = {{Analytic multiplier ideals of toric plurisubharmonic functions on a toric complex space}},
author = {Hoseob Seo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08741},
eprint = {2610.08741},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08741},
}
RIS
TY - UNPB
TI - Analytic multiplier ideals of toric plurisubharmonic functions on a toric complex space
AU - Hoseob Seo
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08741
UR - https://arxiv.org/abs/2610.08741
AB - In this paper, we study analytic multiplier ideal sheaves of toric plurisubharmonic functions on normal affine toric complex analytic spaces equipped with torus-invariant rational divisors, assuming that a positive integer multiple of the log canonical divisor is Cartier. We describe these sheaves in terms of Newton convex bodies and show that they are globally generated by finitely many meromorphic monomials. Our results generalize the description of An and the formulas of Howald and Blickle for monomial ideals, and recover the descriptions of Rashkovskii and Guenancia on affine space. We also extend this description to weights obtained by subtracting positive rational multiples of monomial ideal weights.
ER -