On the Abel-Jacobi map of an elliptic surface and the topology of cubic-line arrangements

Shinzo Bannai; Hiro-o Tokunaga

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arXiv · 1802.06661

On the Abel-Jacobi map of an elliptic surface and the topology of cubic-line arrangements

Shinzo Bannai·Hiro-o Tokunaga

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Abstract

Let $S$ be an elliptic surface over a smooth curve $C$ with a section $O$. We denote its generic fiber by $E_S$. For a divisor $D$ on $S$, we canonically associate a $C(C)$-rational point $P_D$. In this note, we give a description of $P_D$ of $E_S$, when the rank of the group of $C(C)$-rational points is one. We apply our description to refine our result on a Zariski pair for a cubic-line arrangement.

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Shinzo Bannai, Hiro-o Tokunaga. 2018-02-19. On the Abel-Jacobi map of an elliptic surface and the topology of cubic-line arrangements. https://arxiv.org/abs/1802.06661

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