Hermitian Yang-Mills connections on pullback bundles
Abstract
We investigate hermitian Yang-Mills connections on pullback bundles with respect to adiabatic classes on the total space of holomorphic submersions with connected fibres. Under some technical assumptions on the graded object of a Jordan-Holder filtration, we obtain a necessary and sufficient criterion for when the pullback of a strictly semistable vector bundle will carry an hermitian Yang-Mills connection, in terms of intersection numbers on the base of the submersion. Together with the classical Donaldson-Uhlenbeck-Yau correspondence, we deduce that the pullback of a stable (resp. unstable) bundle remains stable (resp. unstable) for adiabatic classes, and settle the semi-stable case.
Cite
@article{arxiv.2006.06453,
title = {Hermitian Yang-Mills connections on pullback bundles},
author = {Lars Martin Sektnan and Carl Tipler},
journal= {arXiv preprint arXiv:2006.06453},
year = {2023}
}
Comments
v.2, fixed gap in previous version under some additional hypotheses