2019/03/18 by Ryushi Goto, Goto, Ryushi
Mathematics · #53C07 #53D17 #53D18 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1903.07425
openalex publication_date 2019/03/18 · openalex created_date 2023/04/07 · openalex updated_date 2026/07/28
In the previous paper \citeGoto2017, the notion of an Einstein-Hermitian metric of a generalized holomorphic vector bundle over a generalized Kahler manifold of symplectic type was introduced from the moment map framework. In this paper we establish a Kobayashi-Hitchin correspondence, that is, the equivalence of the existence of an Einstein-Hermitian metric and ψ-polystability of a generalized holomorphic vector bundle over a compact generalized Kahler manifold of symplectic type. Poisson modules provide intriguing generalized holomorphic vector bundles and we obtain ψ-stable Poisson modules over complex surfaces which are not stable in the ordinary sense.