Browsing by Subject "Fundamental group"

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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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    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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    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.