# 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…

## 9 Citations

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

- Mathematics
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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

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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…

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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…

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. This work is part of a project to construct completions of period mappings Φ : B → Γ \ D . A proper topological SBB-esque completion Φ 0 : B → ℘ 0 is constructed. The ﬁbres of Φ 0 are projective…

Bubbling Phenomenon for Hermitian Yang–Mills Connections

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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…

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

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

Restriction theorems for semistable sheaves

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- 2022

In this paper we prove restriction theorems for torsion-free sheaves that are (semi)stable with respect to the truncated Hilbert polynomial over a smooth projective variety. Our results apply in…

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

- Mathematics
- 2021

. In this paper, we ﬁrst prove a Donaldson-Uhlenbeck-Yau theorem over projective normal varieties smooth in codimension two. As a consequence we deduce the polystability of (dual) tensor products of…

Moduli spaces of slope-semistable pure sheaves

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We construct a moduli space of slope-semistable pure sheaves, building upon previous work of Le Potier and Jun Li on torsion-free sheaves over smooth surfaces. In particular, our construction…

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