On the moduli of logarithmic connections on elliptic curves

TL;DR

This paper studies the moduli spaces of logarithmic rank 2 connections on elliptic curves with multiple poles, focusing on their structure through the analysis of parabolic bundles and their stability properties.

Contribution

It generalizes previous work by providing a detailed description of these moduli spaces using stability analysis of underlying parabolic bundles.

Findings

Characterization of moduli spaces for logarithmic connections on elliptic curves.

Analysis of stability and instability of associated parabolic bundles.

Extension of previous results to cases with multiple poles.

Abstract

We describe moduli spaces of logarithmic rank $2$ connections on elliptic curves with $n \geq 1$ poles and generic residues. In particular, we generalize a previous work by the first and second named authors. Our main approach is to analyze the underlying parabolic bundles; their stability and instability play a major role.