A-infinity algebra of an elliptic curve and Eisenstein series

TL;DR

This paper explicitly computes the A-infinity algebra structure on the Ext-algebra of a specific sheaf collection on an elliptic curve, revealing connections to Eisenstein series and their derivatives.

Contribution

It provides a detailed calculation of the A-infinity structure involving Eisenstein series derivatives, a novel explicit description in this geometric context.

Findings

Explicit A-infinity structure involving Eisenstein series derivatives

Connection between algebraic structures and modular forms

New computational methods for Ext-algebras on elliptic curves

Abstract

We compute explicitly the A-infinity structure on the Ext-algebra of the collection $({\mathcal O}_C, L)$, where $L$ is a line bundle of degree 1 on an elliptic curve $C$. The answer involves higher derivatives of Eisenstein series.