Holomorphic bundles for higher dimensional gauge theory
| Autor: | Jardim, Marcos B., Menet, Gr��goire, Prata, Daniela M., Earp, Henrique N. S�� |
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| Jazyk: | angličtina |
| Rok vydání: | 2011 |
| Předmět: | |
| Popis: | 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. Comment: 19 pages. Final version to appear in Bulletin of the London Mathematical Society |
| Databáze: | OpenAIRE |
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