English

$J$-equation on holomorphic vector bundles

Differential Geometry 2023-11-28 v4

Abstract

We introduce the JJ-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) JJ-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.

Keywords

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

R2 v1 2026-06-24T07:59:44.893Z