The{N/D}-Conjecture for Nonresonant Hyperplane Arrangements
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908773648433152 |
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| author | Xie, Baiting Yu, Chenglong |
| author_facet | Xie, Baiting Yu, Chenglong |
| contents | This paper studies Bernstein--Sato polynomials $b_{f,0}$ for homogeneous polynomials $f$ of degree $d$ with $n$ variables. It is open to know when $-{n\over d}$ is a root of $b_{f,0}$. For essential indecomposable hyperplane arrangements, this is a conjecture by Budur, Mustaţă and Teitler and implies the strong topological monodromy conjecture for arrangements. Walther gave a sufficient condition that a certain differential form does not vanish in the top cohomology group of Milnor fiber. We use Walther's result to verify the $n\over d$-conjecture for weighted hyperplane arrangements satisfying the nonresonant condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05189 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The{N/D}-Conjecture for Nonresonant Hyperplane Arrangements Xie, Baiting Yu, Chenglong Algebraic Geometry Commutative Algebra Combinatorics 32S22 (Primary) 14J17, 14N20, 14F40, 32C38, 32S40 (Secondary) This paper studies Bernstein--Sato polynomials $b_{f,0}$ for homogeneous polynomials $f$ of degree $d$ with $n$ variables. It is open to know when $-{n\over d}$ is a root of $b_{f,0}$. For essential indecomposable hyperplane arrangements, this is a conjecture by Budur, Mustaţă and Teitler and implies the strong topological monodromy conjecture for arrangements. Walther gave a sufficient condition that a certain differential form does not vanish in the top cohomology group of Milnor fiber. We use Walther's result to verify the $n\over d$-conjecture for weighted hyperplane arrangements satisfying the nonresonant condition. |
| title | The{N/D}-Conjecture for Nonresonant Hyperplane Arrangements |
| topic | Algebraic Geometry Commutative Algebra Combinatorics 32S22 (Primary) 14J17, 14N20, 14F40, 32C38, 32S40 (Secondary) |
| url | https://arxiv.org/abs/2501.05189 |