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arXiv · 1508.04300

Mordell-Weil lattices and toric decompositions of plane curves

Remke Kloosterman
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Abstract

We extend results of Cogolludo-Agustin and Libgober relating the Alexander polynomial of a plane curve $C$ with the Mordell--Weil rank of certain isotrivial families of jacobians over $\mathbf{P}^2$ of discriminant $C$. In the second part we introduce a height pairing on the $(2,3,6)$ quasi-toric decompositions of a plane curve. We use this pairing and the results in the first part of the paper to construct a pair of degree 12 curves with 30 cusps and Alexander polynomial $t^2-t+1$, but with distinct height pairing. We use the height pairing to show that these curves from a Zariski pair.

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Remke Kloosterman. 2015-08-18. Mordell-Weil lattices and toric decompositions of plane curves. https://doi.org/10.1007/s00208-016-1399-9

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