On the Alexander invariants of trigonal curves
Date
2021-01-02
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Source Title
Revista Matemática Complutense
Print ISSN
1139-1138
Electronic ISSN
1988-2807
Publisher
Springer - Verlag Italia Srl
Volume
35
Issue
Pages
265 - 286
Language
English
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Abstract
We show that most of the genus-zero subgroups of the braid group B3 (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 “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.