The geometry of three sections on certain rational elliptic surfaces and Mumford representations

TL;DR

This paper explores the geometric properties of plane curves derived from three sections and their sum on rational elliptic surfaces, utilizing Mumford representations to provide new insights and proofs for classical results.

Contribution

It introduces a novel approach using Mumford representations to analyze the geometry of sections on rational elliptic surfaces, offering new proofs for classical results.

Findings

New proofs for classical results on singular plane quartics

Insights into the geometry of sections on rational elliptic surfaces

Application of Mumford representations to study divisors

Abstract

In this article, we study the geometry of plane curves obtained by three sections and another section given as their sum on certain rational elliptic surfaces. We make use of Mumford representations of semi-reduced divisors in order to study the geometry of sections. As a result, we are able to give new proofs for some classical results on singular plane quartics and their bitangent lines.