Homotopy type of complements of fiber-type curves
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908460807880704 |
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| author | Cogolludo-Agustín, José I. Elduque, Eva |
| author_facet | Cogolludo-Agustín, José I. Elduque, Eva |
| contents | In this note we study the homotopy type of the complement of a plane projective curve of fiber-type. Roughly speaking, a curve of fiber-type is a finite union of fibers of a pencil. Under some restrictions, a full description of their homotopy type is given. In the context of fiber-type curves, we also partially answer in the positive a question originally posed by Libgober on the homotopy type of complements of plane curves, namely, whether or not the homotopy type of a curve complement is determined by the fundamental group and its Euler characteristic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16374 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homotopy type of complements of fiber-type curves Cogolludo-Agustín, José I. Elduque, Eva Algebraic Geometry In this note we study the homotopy type of the complement of a plane projective curve of fiber-type. Roughly speaking, a curve of fiber-type is a finite union of fibers of a pencil. Under some restrictions, a full description of their homotopy type is given. In the context of fiber-type curves, we also partially answer in the positive a question originally posed by Libgober on the homotopy type of complements of plane curves, namely, whether or not the homotopy type of a curve complement is determined by the fundamental group and its Euler characteristic. |
| title | Homotopy type of complements of fiber-type curves |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2507.16374 |