On the Alexander invariants of trigonal curves

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Üçer M.

Revista Matematica Complutense, vol.35, no.1, pp.265-286, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 35 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.1007/s13163-020-00381-9
  • Journal Name: Revista Matematica Complutense
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Page Numbers: pp.265-286
  • Keywords: Trigonal curve, Alexander invariant, Braid monodromy, Burau representation, Modular group, Dessin d'enfant
  • Ankara Yıldırım Beyazıt University Affiliated: No

Abstract

© 2021, Universidad Complutense de Madrid.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.