A note on singular Hermitian Yang–Mills connections

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.

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Y.L. is supported by the Engineering and Physical Sciences Research Council [EP/L015234/1], the EPSRC Centre for Doctoral Training in Geometry and Number Theory (The London School of Geometry and Number Theory), University College London. The author is also funded by Imperial College London for his PhD studies.

Received 10 August 2020

Received revised 20 August 2021

Accepted 13 September 2021

Published 21 June 2023