English

Mordell-Weil groups and Zariski triples

Algebraic Geometry 2024-10-22 v1

Abstract

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 general degree dd base change of C12d,mC_{12d,m} and calculate the dimension of the equisingular deformation space.

Keywords

Cite

@article{arxiv.1111.5703,
  title  = {Mordell-Weil groups and Zariski triples},
  author = {Jose Ignacio Cogolludo-Agustin and Remke Kloosterman},
  journal= {arXiv preprint arXiv:1111.5703},
  year   = {2024}
}
R2 v1 2026-06-21T19:40:54.733Z