Browsing by Subject "Plane sextic"

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    Classical Zariski pairs
    (Worldwide Center of Mathematics, 2010) Degtyarev, D.
    We compute the fundamental groups of the complements of all irreducible plane sextics constituting classical Zariski pairs.
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    Classical Zariski pairs
    (2012) Akyol, A.
    We enumerate and classify up to equisingular deformation all irreducible plane sextics constituting the so called classical Zariski pairs. In most cases we obtain two deformation families, called abundant and non-abundant. Four sets of singularities are realized by abundant sextics only, and one exceptional set of singularities is realized by three families, one abundant and two complex conjugate non-abundant. This exceptional set of singularities has submaximal total Milnor number 18. © 2012 World Scientific Publishing Company.
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    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.
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    Oka's conjecture on irreducible plane sextics II
    (2009) Degtyarev, A.
    We complete the proof of Oka's conjecture on the Alexander polynomial of an irreducible plane sextic. We also calculate the fundamental groups of irreducible sextics with a singular point adjacent to J10. © 2009 World Scientific Publishing Company.
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    On plane sextics with double singular points
    (Mathematical Sciences Publishers, 2013) Degtyarev, Alex
    We compute the fundamental groups of five maximizing sextics with double singular points only; in four cases, the groups are as expected. The approach used would apply to other sextics as well, given their equations.
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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.
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    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.