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1 October 2020 Singularities of Hermitian–Yang–Mills connections and Harder–Narasimhan–Seshadri filtrations
Xuemiao Chen, Song Sun
Duke Math. J. 169(14): 2629-2695 (1 October 2020). DOI: 10.1215/00127094-2020-0014


This is the first of a series of papers where we relate tangent cones of Hermitian–Yang–Mills connections at a singularity to the complex algebraic geometry of the underlying reflexive sheaf. In this paper we work on the case when the sheaf is locally modeled on the pullback of a holomorphic vector bundle from the projective space, and 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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Xuemiao Chen. Song Sun. "Singularities of Hermitian–Yang–Mills connections and Harder–Narasimhan–Seshadri filtrations." Duke Math. J. 169 (14) 2629 - 2695, 1 October 2020.


Received: 7 January 2019; Revised: 6 February 2020; Published: 1 October 2020
First available in Project Euclid: 27 August 2020

MathSciNet: MR4149506
Digital Object Identifier: 10.1215/00127094-2020-0014

Primary: 70S15
Secondary: 32G13 , 32Q15 , 53C07

Keywords: Harder–Narasimhan–Seshadri filtrations , Hermitian–Yang–Mills connections , instantons , reflexive sheaves , singularities

Rights: Copyright © 2020 Duke University Press


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Vol.169 • No. 14 • 1 October 2020
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