$J$-equation on holomorphic vector bundles
Differential Geometry
2023-11-28 v4
Abstract
We introduce the -equation on holomorphic vector bundles over compact K\"ahler manifolds and investigate some fundamental properties as well as examples of solutions. In particular, we provide an algebraic condition called (asymptotic) -stability in terms of subbundles on compact K\"ahler surfaces, and a numerical criterion on vortex bundles via dimensional reduction. Also, we discuss an application for the vector bundle version of the deformed Hermitian-Yang-Mills equation in the small volume regime.
Cite
@article{arxiv.2112.00550,
title = {$J$-equation on holomorphic vector bundles},
author = {Ryosuke Takahashi},
journal= {arXiv preprint arXiv:2112.00550},
year = {2023}
}
Comments
52 pages, final version, to appear in J. Funct. Anal