On the Alexander Invariants of Trigonal Curves
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866911070752342016 |
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| author | Üçer, Melih |
| author_facet | Üçer, Melih |
| contents | We show that most of the genus-zero subgroups of the braid group $\mathbb{B}_3$ (which are roughly the braid monodromy groups of the trigonal curves on the Hirzebruch surfaces) are irrelevant as far as the Alexander invariant is concerned: there is a very restricted class of \enquote{primitive} genus-zero subgroups such that these subgroups and their genus-zero intersections determine all the Alexander invariants. Then, we classify the primitive subgroups in a special subclass. This result implies the known classification of the dihedral covers of irreducible trigonal curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_05802 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On the Alexander Invariants of Trigonal Curves Üçer, Melih Algebraic Geometry 14F35 (Primary) 14H50, 20F36, 14H30, 14H57 (Secondary) We show that most of the genus-zero subgroups of the braid group $\mathbb{B}_3$ (which are roughly the braid monodromy groups of the trigonal curves on the Hirzebruch surfaces) are irrelevant as far as the Alexander invariant is concerned: there is a very restricted class of \enquote{primitive} genus-zero subgroups such that these subgroups and their genus-zero intersections determine all the Alexander invariants. Then, we classify the primitive subgroups in a special subclass. This result implies the known classification of the dihedral covers of irreducible trigonal curves. |
| title | On the Alexander Invariants of Trigonal Curves |
| topic | Algebraic Geometry 14F35 (Primary) 14H50, 20F36, 14H30, 14H57 (Secondary) |
| url | https://arxiv.org/abs/2003.05802 |