Wild Character Varieties, points on the Riemann sphere and Calabi's examples

TL;DR

This paper explores basic wild character varieties, connecting them to classical work by Sibuya, Calabi, and Euler, and discusses their representations on the Riemann sphere.

Contribution

It provides new descriptions of wild character varieties and links them to historical mathematical work, enhancing understanding of their structure and significance.

Findings

Descriptions of wild character varieties provided

Connections established with classical mathematical work

Enhanced understanding of their structure and significance

Abstract

We will give several descriptions of some basic examples of wild character varieties, including a discussion of links to work of Sibuya, Calabi and Euler, amongst others.