Mordell–Weil groups and Zariski triples

  • José Ignacio Cogolludo-Agustín

    Universidad de Zaragoza, Spain
  • Remke Kloosterman

    Humboldt-Universität zu Berlin, Germany
Mordell–Weil groups and Zariski triples cover
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We prove the existence of three irreducible curves C12,mC_{12,m} of degree 12 with the same number of cusps and different Alexander polynomials. This exhibits a Zariski triple. Moreover we provide a set of generators for the elliptic threefold with constant jj-invariant 0 and discriminant curve C12,mC_{12,m}. Finally we consider a general degree dd base change of C12d,mC_{12d,m} and calculate the dimension of the equisingular deformation space.