Dunkl connections on $\mathbb{C}^2$ and spherical metrics

TL;DR

This paper investigates Dunkl connections on complex two-dimensional space, revealing they generally do not preserve Hermitian forms, and connects this to the topology of moduli spaces of spherical tori with conical points.

Contribution

It demonstrates the non-preservation of Hermitian forms by Dunkl connections on ^2 and links this to the topology of moduli spaces of spherical tori.

Findings

Dunkl connections on ^2 typically do not preserve Hermitian forms

The topology of the moduli space of spherical tori with one conical point is non-trivial

Recent understanding of moduli space topology informs properties of Dunkl connections

Abstract

We show that general Dunkl connections on $\mathbb{C}^2$ do not preserve non-zero Hermitian forms. Our proof relies on recent understanding of the non-trivial topology of the moduli space of spherical tori with one conical point.