On the Alexander invariants of trigonal curves
Revista Matematica Complutense, cilt.35, sa.1, ss.265-286, 2022 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 35 Sayı: 1
- Basım Tarihi: 2022
- Doi Numarası: 10.1007/s13163-020-00381-9
- Dergi Adı: Revista Matematica Complutense
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
- Sayfa Sayıları: ss.265-286
- Anahtar Kelimeler: Trigonal curve, Alexander invariant, Braid monodromy, Burau representation, Modular group, Dessin d'enfant
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Ankara Yıldırım Beyazıt Üniversitesi Adresli: Evet
Özet
© 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.