Commuting Differential Operators of Rank 3 Associated to a Curve of Genus 2

TL;DR

This paper constructs examples of commuting differential operators of rank 3 linked to a genus 2 curve, advancing understanding of algebraic structures associated with complex curves.

Contribution

It introduces explicit examples of commuting differential operators of rank 3 associated with genus 2 curves, expanding the class of known algebraic operators.

Findings

Constructed explicit examples of commuting differential operators

Linked operators to a specific algebraic curve of genus 2

Enhanced understanding of algebraic structures in differential operator theory

Abstract

In this paper, we construct some examples of commuting differential operators $L_1$ and $L_2$ with rational coefficients of rank 3 corresponding to a curve of genus 2.