Blowing-up Hermitian Yang--Mills connections
Abstract
We investigate hermitian Yang--Mills connections for pullback vector bundles on blow-ups of K\"ahler manifolds along submanifolds. Under some mild asumptions on the graded object of a simple and semi-stable vector bundle, we provide a necessary and sufficent numerical criterion for the pullback bundle to admit a sequence of hermitian Yang--Mills connections for polarisations that make the exceptional divisor sufficiently small, and show that those connections converge to the pulled back hermitian Yang-Mills connection of the graded object.
Cite
@article{arxiv.2301.00525,
title = {Blowing-up Hermitian Yang--Mills connections},
author = {Andrew Clarke and Carl Tipler},
journal= {arXiv preprint arXiv:2301.00525},
year = {2023}
}
Comments
21 pages. Previous Lemma 2.5 was wrong and has been fixed. This required a new approach. Sections 4 and 5 are new, and replace former Sections 3-5. New hypothesis in the main statement regarding the graded object and the codimension of the blown-up locus