में बचाया:
| मुख्य लेखकों: | , |
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| स्वरूप: | Preprint |
| प्रकाशित: |
2024
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| विषय: | |
| ऑनलाइन पहुंच: | https://arxiv.org/abs/2408.02601 |
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| _version_ | 1866911977485369344 |
|---|---|
| author | Bath, Daniel Dakin, Henry |
| author_facet | Bath, Daniel Dakin, Henry |
| contents | We study the canonical Hodge filtration on the sheaf $\mathscr{O}_X(*D)$ of meromorphic functions along a divisor. For a germ of an analytic function $f$ whose Bernstein-Sato's polynomial's roots are contained in $(-2,0)$, we: give a simple algebraic formula for the zeroeth piece of the Hodge filtration; bound the first step of the Hodge filtration containing $f^{-1}$. If we additionally require $f$ to be Euler homogeneous and parametrically prime, then we extend our algebraic formula to compute every piece of the canonical Hodge filtration, proving in turn that the Hodge filtration is contained in the induced order filtration. Finally, we compute the Hodge filtration in many examples and identify several large classes of divisors realizing our theorems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02601 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Hodge filtration and parametrically prime divisors Bath, Daniel Dakin, Henry Algebraic Geometry Commutative Algebra Primary 14J17, 32S35 Secondary: 14F17, 14F10, 32C38, 32S40 We study the canonical Hodge filtration on the sheaf $\mathscr{O}_X(*D)$ of meromorphic functions along a divisor. For a germ of an analytic function $f$ whose Bernstein-Sato's polynomial's roots are contained in $(-2,0)$, we: give a simple algebraic formula for the zeroeth piece of the Hodge filtration; bound the first step of the Hodge filtration containing $f^{-1}$. If we additionally require $f$ to be Euler homogeneous and parametrically prime, then we extend our algebraic formula to compute every piece of the canonical Hodge filtration, proving in turn that the Hodge filtration is contained in the induced order filtration. Finally, we compute the Hodge filtration in many examples and identify several large classes of divisors realizing our theorems. |
| title | The Hodge filtration and parametrically prime divisors |
| topic | Algebraic Geometry Commutative Algebra Primary 14J17, 32S35 Secondary: 14F17, 14F10, 32C38, 32S40 |
| url | https://arxiv.org/abs/2408.02601 |