Tangent cones of Hermitian Yang-Mills connections with isolated singularities

TL;DR

This paper provides a straightforward proof of the uniqueness of tangent cones for singular Hermitian Yang-Mills connections on reflexive sheaves with isolated singularities, focusing on their local models over projective space.

Contribution

It offers a new, simplified proof of tangent cone uniqueness for singular Hermitian Yang-Mills connections on reflexive sheaves at isolated singularities.

Findings

Proves tangent cone uniqueness for singular Hermitian Yang-Mills connections.

Simplifies previous proofs with a direct approach.

Focuses on local models over projective space.

Abstract

We give a simple direct proof of uniqueness of tangent cones for singular projectively Hermitian Yang-Mills connections on reflexive sheaves at isolated singularities modelled on $\mu$-polystable holomorphic bundles over $\mathbf{P}^{n-1}$.