# Complex algebraic compactifications of the moduli space of Hermitian Yang–Mills connections on a projective manifold

@article{Greb2021ComplexAC,
title={Complex algebraic compactifications
of the moduli space of Hermitian Yang–Mills connections on a projective
manifold},
author={Daniel Greb and Benjamin Sibley and Matei Toma and Richard A. Wentworth},
journal={Geometry \& Topology},
year={2021}
}
In this paper we study the relationship between three compactifications of the moduli space of Hermitian-Yang-Mills connections on a fixed Hermitian vector bundle over a projective algebraic manifold of arbitrary dimension. Via the Donaldson-Uhlenbeck-Yau theorem, this space is analytically isomorphic to the moduli space of stable holomorphic vector bundles, and as such it admits an algebraic compactification by Gieseker-Maruyama semistable torsion-free sheaves. A recent construction due to the…
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