On the Tensor Property of Bernstein-Sato Polynomial
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929380106698752 |
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| author | Shi, Quan Zuo, Huaiqing |
| author_facet | Shi, Quan Zuo, Huaiqing |
| contents | We prove the multiplicative Thom-Sebastiani rule for Bernstein-Sato polynomials, answering the longstanding questions of Budur and Popa. We generalize the result to the tensor of two effective divisors on the product of two arbitrary non-singular complex varieties. This also leads to a multiplicative property related to Igusa's strong monodromy conjecture. Moreover, we propose an extension of our result to Bernstein-Sato polynomials for ideals and prove it for monomial ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04121 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Tensor Property of Bernstein-Sato Polynomial Shi, Quan Zuo, Huaiqing Algebraic Geometry 14F10, 13N10, 13A35, 16S32 We prove the multiplicative Thom-Sebastiani rule for Bernstein-Sato polynomials, answering the longstanding questions of Budur and Popa. We generalize the result to the tensor of two effective divisors on the product of two arbitrary non-singular complex varieties. This also leads to a multiplicative property related to Igusa's strong monodromy conjecture. Moreover, we propose an extension of our result to Bernstein-Sato polynomials for ideals and prove it for monomial ideals. |
| title | On the Tensor Property of Bernstein-Sato Polynomial |
| topic | Algebraic Geometry 14F10, 13N10, 13A35, 16S32 |
| url | https://arxiv.org/abs/2406.04121 |