Spectral Curves of Operators with Elliptic Coefficients

TL;DR

This paper introduces a computer-algebra based method to analyze differential operators with elliptic coefficients, leading to explicit descriptions of associated geometric objects like Lame and Halphen curves.

Contribution

It provides a novel computational approach to derive geometric objects related to elliptic differential operators, including explicit forms of Lame and Halphen curves.

Findings

Examples of Lame curves with double reduction

Explicit reduction of theta functions of Halphen curves

Development of a computer-algebra aided method

Abstract

A computer-algebra aided method is carried out, for determining geometric objects associated to differential operators that satisfy the elliptic ansatz. This results in examples of Lame curves with double reduction and in the explicit reduction of the theta function of a Halphen curve.