Year: 2026
Type: preprint
Abstract: We develop a geometric way to uniformly carry out Hörmander's $L^2$-estimates for Hermitian-Yang-Mills connections with bounded energy on Kähler surfaces. We then show the Uhlenbeck convergence of smooth HYM connections on Kähler surfaces can be realized as algebraic convergence inside an analytic flat family. As applications, we prove a continuity theorem for smoothable families and a boundedness result for $μ$-semistable sheaves with fixed topology. We also discuss potential applications for the moduli problem.
Source: arXiv (Cornell University)
Author: Zhou, Keshu
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7216466450