Singularities of Hermitian-Yang-Mills connections and Harder-Narasimhan-Seshadri filtrations

Singularities of Hermitian-Yang-Mills connections and Harder-Narasimhan-Seshadri filtrations

This is the first of a series of papers where we relate tangent cones of Hermitian-Yang-Mills connections at an isolated singularity to the complex algebraic geometry of the underlying reflexive sheaf, when the sheaf is locally modelled on the pull-back of a holomorphic vector bundle from the projec...

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Veröffentlicht in:arXiv.org 2020-12
Hauptverfasser: Chen, Xuemiao, Sun, Song
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Algebra
Cones
Filtration
Mathematics - Differential Geometry
Singularities
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description This is the first of a series of papers where we relate tangent cones of Hermitian-Yang-Mills connections at an isolated singularity to the complex algebraic geometry of the underlying reflexive sheaf, when the sheaf is locally modelled on the pull-back of a holomorphic vector bundle from the projective space. In this paper we shall impose an extra assumption that the graded sheaf determined by the Harder-Narasimhan-Seshadri filtrations of the vector bundle is reflexive. In general we conjecture that the tangent cone is uniquely determined by the double dual of the associated graded object of a Harder-Narasimhan-Seshadri filtration of an algebraic tangent cone, which is a certain torsion-free sheaf on the projective space. In this paper we also prove this conjecture when there is an algebraic tangent cone which is locally free and stable.
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subjects Algebra
Cones
Filtration
Mathematics - Differential Geometry
Singularities
title Singularities of Hermitian-Yang-Mills connections and Harder-Narasimhan-Seshadri filtrations
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