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arXiv · 2003.05802

On the Alexander Invariants of Trigonal Curves

Melih Üçer
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Abstract

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.

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Melih Üçer. 2020-03-08. On the Alexander Invariants of Trigonal Curves. https://doi.org/10.1007/s13163-020-00381-9

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