# A note on singular Hermitian Yang-Mills connections

## TL;DR

This paper presents an example of a homogeneous reflexive sheaf over complex three-space that admits a non-conical Hermitian Yang-Mills connection, providing insight into bubbling phenomena in complex geometry.

## Contribution

It introduces a specific example of a sheaf with a non-conical Hermitian Yang-Mills connection, advancing understanding of singularity models in complex differential geometry.

## Key findings

- Example of a homogeneous reflexive sheaf with a non-conical Hermitian Yang-Mills connection
- Insights into bubbling phenomena along complex codimension 2 submanifolds
- Modeling of bubbling behavior in complex geometric settings

## Abstract

We give an example of a homogeneous reflexive sheaf over $\mathbb{C}^3$ which admits a non-conical Hermitian Yang-Mills connection. This is expected to model bubbling phenomenon along complex codimension 2 submanifolds when the Fueter section takes zero value.