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.
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