On Poincaré polynomials for plane curves with quasi-homogeneous singularities
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909738747297792 |
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| author | Pokora, Piotr |
| author_facet | Pokora, Piotr |
| contents | We define a combinatorial object that can be associated with any conic-line arrangement with ordinary singularities, which we call the combinatorial Poincaré polynomial. We prove a Terao-type factorization statement on the splitting of such a polynomial over the rationals under the assumption that our conic-line arrangements are free and admit ordinary quasi-homogeneous singularities. Then we focus on the so-called $d$-arrangements in the plane. In particular, we provide a combinatorial constraint for free $d$-arrangements admitting ordinary quasi-homogeneous singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08436 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Poincaré polynomials for plane curves with quasi-homogeneous singularities Pokora, Piotr Algebraic Geometry Combinatorics 14H50, 14N20, 32S25 We define a combinatorial object that can be associated with any conic-line arrangement with ordinary singularities, which we call the combinatorial Poincaré polynomial. We prove a Terao-type factorization statement on the splitting of such a polynomial over the rationals under the assumption that our conic-line arrangements are free and admit ordinary quasi-homogeneous singularities. Then we focus on the so-called $d$-arrangements in the plane. In particular, we provide a combinatorial constraint for free $d$-arrangements admitting ordinary quasi-homogeneous singularities. |
| title | On Poincaré polynomials for plane curves with quasi-homogeneous singularities |
| topic | Algebraic Geometry Combinatorics 14H50, 14N20, 32S25 |
| url | https://arxiv.org/abs/2412.08436 |