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PreprintCC BY-NC-ND 4.0arXiv

Analytic Criteria for Detecting Bernstein-Sato Roots

  • Yifan Chen
  • Huaiqing Zuo
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Abstract

We study roots of Bernstein-Sato polynomials of ideals. Our first main result gives a general partial differential equation criterion for detecting roots of the Bernstein-Sato polynomial of an ideal. For homogeneous case, we recast this criterion as an analytic condition, connecting the algebraic problem of locating roots with analytic properties of the defining data. As an application, we give a series of roots for the general determinantal ideal prove the strong monodromy conjecture for them. Keywords. Bernstein-Sato polynomial, determinantal variety, monodromy conjecture.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026analytic,
  title = {{Analytic Criteria for Detecting Bernstein-Sato Roots}},
  author = {Yifan Chen and Huaiqing Zuo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.14083},
  eprint = {2610.14083},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.14083},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Analytic Criteria for Detecting Bernstein-Sato Roots
AU  - Yifan Chen
AU  - Huaiqing Zuo
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.14083
UR  - https://arxiv.org/abs/2610.14083
AB  - We study roots of Bernstein-Sato polynomials of ideals. Our first main result gives a general partial differential equation criterion for detecting roots of the Bernstein-Sato polynomial of an ideal. For homogeneous case, we recast this criterion as an analytic condition, connecting the algebraic problem of locating roots with analytic properties of the defining data. As an application, we give a series of roots for the general determinantal ideal prove the strong monodromy conjecture for them. Keywords. Bernstein-Sato polynomial, determinantal variety, monodromy conjecture.
ER  -