# Holomorphic bundles for higher dimensional gauge theory

@article{Jardim2011HolomorphicBF,
title={Holomorphic bundles for higher dimensional gauge theory},
author={Marcos Jardim and Gr'egoire Menet and Daniela Moura Prata and Henrique N. S{\'a} Earp},
journal={Bulletin of the London Mathematical Society},
year={2011},
volume={49}
}
• Published 13 September 2011
• Mathematics
• Bulletin of the London Mathematical Society
Motivated by gauge theory under special holonomy, we present techniques to produce holomorphic bundles over certain non‐compact 3‐folds, called building blocks, satisfying a stability condition ‘at infinity’. Such bundles are known to parametrize solutions of the Yang–Mills equation over the G2 ‐manifolds obtained from asymptotically cylindrical Calabi–Yau 3‐folds studied by Kovalev, Haskins et al. and Corti et al. The most important tool is a generalization of Hoppe's stability criterion to…
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## References

SHOWING 1-10 OF 22 REFERENCES

### G2–instantons Over Asymptotically Cylindrical Manifolds

A concrete model for a 7-dimensional gauge theory under special holonomy is proposed, within the paradigm outlined by Donaldson and Thomas, over the asymptotically cylindrical G2-manifolds provided

### K3 surfaces with non-symplectic involution and compact irreducible G2-manifolds

• Mathematics
Mathematical Proceedings of the Cambridge Philosophical Society
• 2011
Abstract We consider the connected-sum method of constructing compact Riemannian 7-manifolds with holonomy G2 developed by the first named author. The method requires pairs of projective complex

### G2-instantons over twisted connected sums

• Mathematics
• 2013
We introduce a method to construct G2 ‐instantons over compact G2 ‐manifolds arising as the twisted connected sum of a matching pair of building blocks. Our construction is based on gluing G2

### G2-manifolds and associative submanifolds via semi-Fano 3-folds

• Mathematics
• 2012
We construct many new topological types of compact G_2-manifolds, i.e. Riemannian 7-manifolds with holonomy group G_2. To achieve this we extend the twisted connected sum construction first developed

### Instanton sheaves on complex projective spaces

We study a class of torsion-free sheaves on complex projective spaces which generalize the much studied mathematical instanton bundles. Instanton sheaves can be obtained as cohomologies of linear

### Complex Projective Geometry: Fano 3-folds

In the beginning of this century, G. Fano initiated the study of 3-dimensional projective varieties X2g−2 ⊂ P with canonical curve sections in connection with the Lüroth problem. After a quick review

### Asymptotically cylindrical Calabi-Yau manifolds

• Mathematics
• 2012
Let M be a complete Ricci-flat Kahler manifold with one end and assume that this end converges at an exponential rate to [0,oo) x X for some compact connected Ricci-flat manifold X. We begin by

### Stability of Special Instanton Bundles on ℙ 2n + 1

• Mathematics
• 1994
We prove that the special instanton bundles of rank 2n on p2n+ 1 (C) with a symplectic structure studied by Spindler and Trautmann are stable in the sense of Mumford-Takemoto. This implies that the

### Asymptotically cylindrical Calabi–Yau 3–folds from weak Fano 3–folds

• Mathematics
• 2012
We prove the existence of asymptotically cylindrical (ACyl) Calabi–Yau 3–folds starting with (almost) any deformation family of smooth weak Fano 3–folds. This allow us to exhibit hundreds of