Browsing by Subject "Dessin d’enfant"

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    Alexander modules of trigonal curves
    (2021-01) Üçer, Melih
    We classify the monodromy Alexander modules of non-isotrivial trigonal curves.
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    On the Alexander invariants of trigonal curves
    (Springer - Verlag Italia Srl, 2021-01-02) Üçer, Melih
    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.
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    Plane sextics with a type e8 singular point
    (Tohoku Daigaku Suugaku Kyoshitsu, 2010) Degtyarev, A.
    We construct explicit geometric models for and compute the fundamental groups of all plane sextics with simple singularities only and with at least one type E8 singular point. In particular, we discover four new sextics with nonabelian fundamental groups; two of them are irreducible. The groups of the two irreducible sextics found are finite. The principal tool used is the reduction to trigonal curves and Grothendieck’s dessins d’enfants.