$J$-equation on holomorphic vector bundles

Abstract

We introduce the $J$-equation on holomorphic vector bundles over compact Kähler manifolds and investigate some fundamental properties as well as examples of solutions. In particular, we provide an algebraic condition called (asymptotic) $J$-stability in terms of subbundles on compact Kähler 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.

arXiv comment52 pages, final version, to appear in J. Funct. Anal