Browsing by Subject "Zariski pair"
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Item Open Access 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.Item Open Access 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.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.