# 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…

## 7 Citations

Continuity of the Yang–Mills flow on the set of semistable bundles

- Mathematics
- 2019

A recent paper (arxiv.org:1810.00025) studied properties of a compactification of the moduli space of irreducible Hermitian-Yang-Mills connections on a hermitian bundle over a projective algebraic…

Compactness for $\Omega$-Yang-Mills connections

- Mathematics
- 2021

On a Riemannian manifold of dimension n we extend the known analytic results on Yang-Mills connections to the class of connections called Ω-Yang-Mills connections, where Ω is a smooth, not…

A Donaldson-Uhlenbeck-Yau theorem for normal varieties and semistable bundles on degenerating families

- Mathematics
- 2021

In this paper, we prove a singular version of the DonaldsonUhlenbeck-Yau theorem over normal projective varieties and normal complex subvarieties of compact Kähler manifolds that are smooth outside a…

A note on singular Hermitian Yang-Mills connections

- Mathematics
- 2019

We give an example of a homogeneous reflexive sheaf over $\mathbb{C}^3$ which admits a non-conical Hermitian Yang-Mills connection. This is expected to model bubbling phenomenon along complex…

Bubbling Phenomenon for Hermitian Yang–Mills Connections

- Mathematics
- 2019

We construct local examples of singular Hermitian Yang-Mills connections over $B_1\subset \mathbb{C}^3$ with uniformly bounded $L^2$-energy, but the number of essential singular points can be…

Towards a maximal completion of a period map

- Mathematics
- 2020

The motivation behind this work is to construct a “Hodge theoretically maximal” completion of a period map. This is done up to finite data (we work with the Stein factorization of the period map).…

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

- MathematicsInventiones mathematicae
- 2021

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

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