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

2018/02/19 by Shinzo Bannai, Bannai, Shinzo, Hiro‐o Tokunaga +1
Mathematics · #14F35 14F45 #14J29 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT)

paper · pdf · doi:10.48550/arxiv.1802.06661

openalex publication_date 2018/02/19 · openalex created_date 2018/03/06 · openalex updated_date 2026/07/28

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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