Holomorphic bundles for higher dimensional gauge theory
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 YangMills equation over the $\rm G_2$manifolds obtained from asymptotically cylindrical CalabiYau $3$folds studied by Kovalev and by CortiHaskinsNordströmPacini 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 blowup phenomenon along a sequence of asymptotically stable bundles degenerating into a torsionfree sheaf.
 Publication:

arXiv eprints
 Pub Date:
 September 2011
 arXiv:
 arXiv:1109.2750
 Bibcode:
 2011arXiv1109.2750J
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Differential Geometry;
 14J60;
 53C07
 EPrint:
 19 pages. Final version to appear in Bulletin of the London Mathematical Society