Reflexive sheaves, Hermitian-Yang-Mills connections, and tangent cones

TL;DR

This paper provides a comprehensive algebraic description of tangent cones of Hermitian-Yang-Mills connections on reflexive sheaves, linking complex geometry and algebraic geometry.

Contribution

It offers a complete algebro-geometric characterization of tangent cones for admissible Hermitian-Yang-Mills connections on reflexive sheaves, advancing understanding in complex differential geometry.

Findings

Algebraic description of tangent cones established

Connection between Hermitian-Yang-Mills connections and algebraic geometry clarified

Framework applicable to all reflexive sheaves

Abstract

In this paper we give a complete algebro-geometric characterization of analytic tangent cones of admissible Hermitian-Yang-Mills connections over any reflexive sheaves.