A new proof of the Caporaso-Sernesi theorem via Weber's formula

TL;DR

This paper presents a novel proof of the Caporaso-Sernesi theorem, demonstrating that a general plane quartic can be uniquely identified by its 28 bitangents using classical geometry and Weber's formula.

Contribution

It introduces a new proof leveraging Weber's formula and the injectivity of the theta map, offering an alternative to existing proofs.

Findings

The general plane quartic is uniquely determined by its 28 bitangents.

Weber's formula and theta map injectivity are key to the proof.

Provides a classical geometric approach to a modern algebraic geometry problem.

Abstract

In this paper we give a new proof of Caporaso and Sernesi's result which states that the general plane quartic is uniquely determined by its 28 bitangents. Our proof uses classical geometric results, as it is based on Weber's formula and on the injectivity of the $\theta^{(4)}$ map.