Holomorphic bundles for higher dimensional gauge theory

Abstract : 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 $G_2$-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 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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https://hal.archives-ouvertes.fr/hal-01675346
Contributor : Imb - Université de Bourgogne <>
Submitted on : Thursday, January 4, 2018 - 1:31:22 PM
Last modification on : Friday, January 5, 2018 - 1:03:24 AM

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Marcos Jardim, Grégoire Menet, Daniela M. Prata, Henrique N. Sá Earp. Holomorphic bundles for higher dimensional gauge theory. Bulletin of the London Mathematical Society, London Mathematical Society, 2017, 49 (1), pp.117-132. ⟨10.1112/blms.12017⟩. ⟨hal-01675346⟩

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