Multiplicative Thom-Sebastiani for Bernstein-Sato polynomials
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913567474712576 |
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| author | Lee, Jonghyun |
| author_facet | Lee, Jonghyun |
| contents | We show that if $f\in \mathcal{O}_X(X)$ and $g\in \mathcal{O}_Y(Y)$ are nonzero regular functions on smooth complex algebraic varieties $X$ and $Y$, then the Bernstein-Sato polynomial of the product function $fg \in \mathcal{O}_{X\times Y}(X \times Y)$ is given by $b_{fg}(s)=b_f(s)b_g(s)$, answering a question of Budur and Popa. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04512 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multiplicative Thom-Sebastiani for Bernstein-Sato polynomials Lee, Jonghyun Algebraic Geometry 14F10 (Primary) We show that if $f\in \mathcal{O}_X(X)$ and $g\in \mathcal{O}_Y(Y)$ are nonzero regular functions on smooth complex algebraic varieties $X$ and $Y$, then the Bernstein-Sato polynomial of the product function $fg \in \mathcal{O}_{X\times Y}(X \times Y)$ is given by $b_{fg}(s)=b_f(s)b_g(s)$, answering a question of Budur and Popa. |
| title | Multiplicative Thom-Sebastiani for Bernstein-Sato polynomials |
| topic | Algebraic Geometry 14F10 (Primary) |
| url | https://arxiv.org/abs/2402.04512 |