Browsing by Subject "Trigonal curve"
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Item Open Access Alexander modules of trigonal curves(Bilkent University, 2021-01) Üçer, MelihWe classify the monodromy Alexander modules of non-isotrivial trigonal curves.Item Open Access Irreducible plane sextics with large fundamental groups(Japan Society of Mathematical Education,Nippon Sugaku Kyoiku Gakkai, 2009) Degtyarev, A.We compute the fundamental group of the complement of each irreducible sextic of weight eight or nine (in a sense, the largest groups for irreducible sextics), as well as of 169 of their derivatives (both of and not of torus type). We also give a detailed geometric description of sextics of weight eight and nine and of their moduli spaces and compute their Alexander modules; the latter are shown to be free over an appropriate ring. © 2009 The Mathematical Society of Japan.Item Open Access On the Alexander invariants of trigonal curves(Springer - Verlag Italia Srl, 2021-01-02) Üçer, MelihWe 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.Item Open Access 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.Item Open Access Stable symmetries of plane sextics(Springer Netherlands, 2008) Degtyarev, A.We classify projective symmetries of irreducible plane sextics with simple singularities which are stable under equivariant deformations. We also outline a connection between order 2 stable symmetries and maximal trigonal curves. © 2008 Springer Science+Business Media B.V.Item Open Access 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.