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arXiv · 2005.12673

Torsion divisors of plane curves with maximal flexes and Zariski pairs

E. Artal Bartolo·S. Bannai·T. Shirane·H. Tokunaga
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Abstract

There is a close relationship between the embedded topology of complex plane curves and the (group-theoretic) arithmetic of elliptic curves. In a recent paper, we studied the topology of some arrangements of curves which include a special smooth component, via the torsion properties induced by the divisors in the special curve associated to the remaining components, which is an arithmetic property. When this special curve has maximal flexes, there is a natural isomorphism between its Jacobian variety and the degree zero part of its Picard group. In this paper we consider curve arrangements which contain a special smooth component with a maximal flex and exploit these properties to obtain Zariski tuples which show the interplay between topology, geometry and arithmetic.

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E. Artal Bartolo, S. Bannai, T. Shirane, H. Tokunaga. 2020-05-26. Torsion divisors of plane curves with maximal flexes and Zariski pairs. https://arxiv.org/abs/2005.12673

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