PreprintCC BY 4.0arXiv
Limiting properties of Hermitian-Einstein metrics under variation of the Kähler class
Abstract
We study the behaviour of Hermitian-Einstein metrics on a holomorphic vector bundle over a compact Kähler manifold, as the underlying Kähler metric varies and its Kähler class changes. In particular, if the bundle stops being stable at some point, the Hermitian-Einstein metrics blow up, and their rescaling can be used to construct a destabilizing subsheaf, following the argument of Uhlenbeck and Yau. Furthermore, we study the behaviour of Chern connections of these metrics, and show, that after passing to a subsequence, and applying suitable gauge transforms these connections converge, and identify the blow-up locus of their Uhlenbeck limit.
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BibTeX
@misc{klemyatin2026limiting,
title = {{Limiting properties of Hermitian-Einstein metrics under variation of the Kähler class}},
author = {Nikita Klemyatin},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03025},
eprint = {2611.03025},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03025},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Limiting properties of Hermitian-Einstein metrics under variation of the Kähler class
AU - Nikita Klemyatin
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03025
UR - https://arxiv.org/abs/2611.03025
AB - We study the behaviour of Hermitian-Einstein metrics on a holomorphic vector bundle over a compact Kähler manifold, as the underlying Kähler metric varies and its Kähler class changes. In particular, if the bundle stops being stable at some point, the Hermitian-Einstein metrics blow up, and their rescaling can be used to construct a destabilizing subsheaf, following the argument of Uhlenbeck and Yau. Furthermore, we study the behaviour of Chern connections of these metrics, and show, that after passing to a subsequence, and applying suitable gauge transforms these connections converge, and identify the blow-up locus of their Uhlenbeck limit.
ER -