First homology groups of the Milnor fiber boundary for generic hyperplane arrangements in $\mathbb{C}^{3}$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866918138435600384 |
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| author | Sugawara, Sakumi |
| author_facet | Sugawara, Sakumi |
| contents | We study the Milnor fiber boundary for hyperplane arrangements in $\mathbb{C}^3$. This is one of the examples of non-isolated surface singularities, which are studied by Némethi--Szilárd. In this paper, we compute the first homology group of the Milnor fiber boundary for a generic arrangement, which gives an affirmative answer to the conjecture of Suciu. Also, we give an example of an arrangement with $n$ hyperplanes, whose torsion part in the Milnor fiber boundary homology contains a direct summand other than $\mathbb{Z}_{n}$, for certain value of $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01555 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | First homology groups of the Milnor fiber boundary for generic hyperplane arrangements in $\mathbb{C}^{3}$ Sugawara, Sakumi Geometric Topology Algebraic Geometry Combinatorics 32S22, 32S55, 52C35 We study the Milnor fiber boundary for hyperplane arrangements in $\mathbb{C}^3$. This is one of the examples of non-isolated surface singularities, which are studied by Némethi--Szilárd. In this paper, we compute the first homology group of the Milnor fiber boundary for a generic arrangement, which gives an affirmative answer to the conjecture of Suciu. Also, we give an example of an arrangement with $n$ hyperplanes, whose torsion part in the Milnor fiber boundary homology contains a direct summand other than $\mathbb{Z}_{n}$, for certain value of $n$. |
| title | First homology groups of the Milnor fiber boundary for generic hyperplane arrangements in $\mathbb{C}^{3}$ |
| topic | Geometric Topology Algebraic Geometry Combinatorics 32S22, 32S55, 52C35 |
| url | https://arxiv.org/abs/2404.01555 |