Browsing by Subject "Braid monodromy"

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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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    Zariski k-plets via dessins d ' enfants
    (2009) Degtyarev, A.
    We construct exponentially large collections of pairwise distinct equisingular deformation families of irreducible plane curves sharing the same sets of singularities. The fundamental groups of all curves constructed are abelian. © Swiss Mathematical Society.