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$J$-equation on holomorphic vector bundles

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arxiv 2112.00550 v4 pith:NKS56QKZ submitted 2021-12-01 math.DG

Ryosuke Takahashi This is my paper · ORCID
classification math.DG
keywords bundlesequationvectorahlercompactholomorphicalgebraicapplication
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abstract

We introduce the $J$-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) $J$-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.

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  1. Perturbations of Vector Bundle whose Curvature Form Solves a Polynomial Equation

    math.DG 2025-07 conditional novelty 8.0 of 10

    Local existence of solutions to polynomial curvature equations is equivalent to local polystability, with local filtrations and a Kempf-Ness homeomorphism.

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