# The matroid structure of vectors of the Mordell-Weil lattice and the topology of plane quartics and bitangent lines

## TL;DR

This paper explores the matroid structure of vectors in the Mordell-Weil lattice to analyze the topology of plane quartics and bitangent lines, providing new examples of Zariski N-ples with low degrees.

## Contribution

It introduces matroid terminology into the study of Zariski-pairs, simplifying the approach and enabling the construction of new low-degree Zariski N-ples.

## Key findings

- Existence of a Zariski 102-ple of degree 18
- Matroid framework simplifies topology analysis of quartics
- New examples of Zariski N-ples with low degree

## Abstract

In this paper, we introduce the terminology of matroids into the study of Zariski-pairs related to rational elliptic surfaces, aiming to simplify the presentation and arguments involved. As an application, we provide new examples of Zariski $N$-ples of relatively low degree. Namely we show that a Zariski 102-ple of degree 18 exists.