On the Abel-Jacobi map for bisections of rational elliptic surfaces and Zariski $N$-plet for conic arrangements

TL;DR

This paper investigates the Abel-Jacobi map for bisections on rational elliptic surfaces and uses this to construct examples of Zariski N-plets for conic arrangements, revealing new geometric configurations.

Contribution

It introduces a novel application of the Abel-Jacobi map to construct Zariski N-plets for conic arrangements, linking elliptic surface theory with algebraic geometry.

Findings

Construction of Zariski N-plets for conic arrangements

New insights into the Abel-Jacobi map for rational elliptic surfaces

Examples illustrating the geometric complexity of conic arrangements

Abstract

We study the Abel-Jacobi map for bisections of a certain rational elliptic surface. As an application, we construct examples of Zariski $N$-plets for conic arrangements.