Hermitian Yang-Mills connections on pullback bundles


Abstract in English

We investigate stability of pullback bundles with respect to adiabatic classes on the total space of holomorphic submersions. We show that the pullback of a stable (resp. unstable) bundle remains stable (resp. unstable) for these classes. Assuming the graded object of a Jordan-Holder filtration to be locally free, we obtain a necessary and sufficient criterion for when the pullback of a strictly semistable vector bundle will be stable, in terms of intersection numbers on the base of the fibration. The arguments rely on adiabatic constructions of hermitian Yang-Mills connections together with the classical Donaldson-Uhlenbeck-Yau correspondence.

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