CAT(0) geometry of complex curve complements and families
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913587524534272 |
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| author | Bregman, Corey Libgober, Anatoly Zhu, Kejia |
| author_facet | Bregman, Corey Libgober, Anatoly Zhu, Kejia |
| contents | Motivated by the question of whether braid groups are CAT(0), we investigate the CAT(0) behavior of fundamental groups of plane curve complements and certain universal families. If $C$ is the branch locus of a generic projection of a smooth, complete intersection surface to $\PP^2$, we show that $π_1(\PP^2\setminus C)$ is CAT(0). In the other direction, we prove that the fundamental group of the universal family associated with the singularities of type $E_6$, $E_7$, and $E_8$ is not CAT(0). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18067 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | CAT(0) geometry of complex curve complements and families Bregman, Corey Libgober, Anatoly Zhu, Kejia Geometric Topology Algebraic Geometry Group Theory Motivated by the question of whether braid groups are CAT(0), we investigate the CAT(0) behavior of fundamental groups of plane curve complements and certain universal families. If $C$ is the branch locus of a generic projection of a smooth, complete intersection surface to $\PP^2$, we show that $π_1(\PP^2\setminus C)$ is CAT(0). In the other direction, we prove that the fundamental group of the universal family associated with the singularities of type $E_6$, $E_7$, and $E_8$ is not CAT(0). |
| title | CAT(0) geometry of complex curve complements and families |
| topic | Geometric Topology Algebraic Geometry Group Theory |
| url | https://arxiv.org/abs/2411.18067 |