PreprintCC BY-NC-ND 4.0arXiv
Bernstein--Sato ideals might not be linear
Abstract
Let F=(f1,…,fr) be a family of nonzero polynomials on ℂn. More than ten years ago, Budur conjectured that BF, the Bernstein--Sato ideal of F, is generated by products of linear polynomials with rational coefficients. With the aid of AI, we construct two counterexamples to Budur's conjecture. The examples indicate that main results in [Wu26] provide the optimal linearity properties that the zero locus of Bernstein-Sato ideals satisfies in general.
Related
- Zero loci of Bernstein-Sato ideals are not necessarily linear
- On the Multiplicative Thom-Sebastiani Property for Bernstein-Sato Polynomials of Ideals
- Bernstein-Sato polynomials of generic Pfaffian ideals
- A Polynomial PDE Criterion for the −n/d Root of the Bernstein-Sato polynomial of Homogeneous Ideals
- Bounds for Codimension-One Components of Zero Loci of Bernstein-Sato Ideals
BibTeX
@misc{wu2026bernsteinsato,
title = {{Bernstein--Sato ideals might not be linear}},
author = {Lei Wu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32287},
eprint = {2609.32287},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32287},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Bernstein--Sato ideals might not be linear
AU - Lei Wu
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32287
UR - https://arxiv.org/abs/2609.32287
AB - Let F=(f_1,…,f_r) be a family of nonzero polynomials on ℂ^n. More than ten years ago, Budur conjectured that B_F, the Bernstein--Sato ideal of F, is generated by products of linear polynomials with rational coefficients. With the aid of AI, we construct two counterexamples to Budur's conjecture. The examples indicate that main results in [Wu26] provide the optimal linearity properties that the zero locus of Bernstein-Sato ideals satisfies in general.
ER -