Analytic tangent cones of admissible Hermitian-Yang-Mills connections

TL;DR

This paper investigates the local behavior of Hermitian-Yang-Mills connections near singularities, linking tangent cones to filtrations and providing geometric insights into bubbling phenomena.

Contribution

It introduces a detailed analysis of tangent cones of admissible Hermitian-Yang-Mills connections and relates them to algebraic filtrations, extending previous results.

Findings

Characterization of tangent cones near singularities.

Relation between tangent cones and Harder-Narasimhan-Seshadri filtration.

Algebro-geometric description of bubbling set.

Abstract

In this paper we study the analytic tangent cones of admissible Hermitian-Yang-Mills connections near a homogeneous singularity of a reflexive sheaf, and relate it to the Harder-Narasimhan-Seshadri filtration. We also give an algebro-geometric characterization of the bubbling set. This strengthens our previous result.