Monad constructions of asymptotically stable bundles

Details Monad constructions of asymptotically stable bundles Monad constructions of asymptotically stable bundles

2011-09-13

arxiv.org/abs/1109.2750v1

Mathematics

Algebraic Geometry

14 pages, 1 figure

Scientific paper

Motivated by by gauge theory on G2-manifolds, we produce several examples of bundles satisfying an `asymptotic' stability condition over a divisor `at infinity' over certain Fano 3-folds with exceptional holonomy studied by A. Kovalev. Such bundles are known to parametrise solutions of the Yang-Mills equation over the compact G2-manifolds obtained from the initial Fanos by a twisted connected sum operation. One of our tools is a generalisation 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.

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