Hermitian-Yang-Mills connections on collapsing elliptically fibered $K3$ surfaces
Differential Geometry
2022-08-11 v2
Abstract
Let be an elliptically fibered surface, admitting a sequence of Ricci-flat metrics collapsing the fibers. Let be a holomorphic bundle over , stable with respect to . Given the corresponding sequence of Hermitian-Yang-Mills connections on , we prove that, if is a generic fiber, the restricted sequence converges to a flat connection . Furthermore, if the restriction is of the form for distinct points , then these points uniquely determine .
Keywords
Cite
@article{arxiv.1710.03898,
title = {Hermitian-Yang-Mills connections on collapsing elliptically fibered $K3$ surfaces},
author = {Ved Datar and Adam Jacob},
journal= {arXiv preprint arXiv:1710.03898},
year = {2022}
}
Comments
This version contains new notation, further expository details, and a breaking of the main result into a Theorem and Corollary, as suggested by the referee