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arXiv · 1109.2750

Holomorphic bundles for higher dimensional gauge theory

Marcos B. Jardim·Grégoire Menet·Daniela M. Prata·Henrique N. Sá Earp
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Abstract

Motivated by gauge theory under special holonomy, we present techniques to produce holomorphic bundles over certain noncompact $3-$folds, called building blocks, satisfying a stability condition `at infinity'. Such bundles are known to parametrise solutions of the Yang-Mills equation over the $\rm G_2-$manifolds obtained from asymptotically cylindrical Calabi-Yau $3-$folds studied by Kovalev and by Corti-Haskins-Nordstr\"om-Pacini et al. The most important tool is a generalisation of Hoppe's stability criterion to holomorphic bundles over smooth projective varieties $X$ with $\operatorname{Pic}{X}\simeq\mathbb{Z}^l$, a result which may be of independent interest. Finally, we apply monads to produce a prototypical model of the curvature blow-up phenomenon along a sequence of asymptotically stable bundles degenerating into a torsion-free sheaf.

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Marcos B. Jardim, Grégoire Menet, Daniela M. Prata, Henrique N. Sá Earp. 2011-09-13. Holomorphic bundles for higher dimensional gauge theory. https://doi.org/10.1112/blms.12017

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