Semi-stability and local wall-crossing for hermitian Yang-Mills connections
Differential Geometry
2023-04-12 v1 Algebraic Geometry
Abstract
We consider a sufficiently smooth semi-stable holomorphic vector bundle over a compact K\"ahler manifold. Assuming the automorphism group of its graded object to be abelian, we provide a semialgebraic decomposition of a neighbourhood of the polarisation in the K\"ahler cone into chambers characterising (in)stability. For a path in a stable chamber converging to the initial polarisation, we show that the associated HYM connections converge to an HYM connection on the graded object.
Keywords
Cite
@article{arxiv.2304.05245,
title = {Semi-stability and local wall-crossing for hermitian Yang-Mills connections},
author = {Andrew Clarke and Carl Tipler},
journal= {arXiv preprint arXiv:2304.05245},
year = {2023}
}
Comments
15 pages, comments very welcome. arXiv admin note: substantial text overlap with arXiv:2301.00525