Ulrich Bundles on Elliptic Curves and Theta Functions

TL;DR

This paper explicitly constructs Ulrich bundles on elliptic curves embedded as Hesse cubics using Moore matrices and theta functions, providing concrete algebraic descriptions.

Contribution

It introduces a novel explicit method to present Ulrich bundles on elliptic curves via Moore matrices and theta functions, enhancing understanding of their structure.

Findings

Explicit presentation of Ulrich bundles on elliptic curves.

Connection between Moore matrices, theta functions, and Ulrich bundles.

Enhanced algebraic understanding of Ulrich bundles on elliptic curves.

Abstract

Let $E$ be a smooth elliptic curve over $\mathbb{C}$. For $E$ embedded into $\mathbb{P}^2$ as Hesse cubic and $V$ an Ulrich bundle on $E$ we derive a explicit presentation of $V$ using Moore matrices and theta functions.