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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    Pic  X  ≃   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.

Holomorphic bundles for higher dimensional gauge theory