Semi-stability and local wall-crossing for hermitian Yang-Mills connections

Abstract

We consider a sufficiently smooth semi-stable holomorphic vector bundle over a compact Kähler 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 Kähler 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.

15 pages, comments very welcome. arXiv admin note: substantial text overlap with arXiv:2301.00525