Browsing by Subject "Fundamental Group"

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    The Alexander module of a trigonal curve
    (Eurpean Mathematical Society, 2014) Degtyarev, A.
    We describe the Alexander modules and Alexander polynomials (both over ℚ and over finite fields Fp) of generalized trigonal curves. The rational case is completely resolved; in the case of characteristic p > 0, a few points remain open. The results obtained apply as well to plane curves with deep singularities. © European Mathematical Society.
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    On plane sextics with double singular points
    (2013) Degtyarev, A.
    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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    On the Artal-Carmona-Cogolludo construction
    (World Scientific Publishing, 2014) Degtyarev, A.
    We derive explicit defining equations for a number of irreducible maximizing plane sextics with double singular points only. For most real curves, we also compute the fundamental group of the complement; all groups found are abelian, which suffices to complete the computation of the groups of all non-maximizing irreducible sextics. As a by-product, examples of Zariski pairs in the strongest possible sense are constructed. © 2014 World Scientific Publishing Company.