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arXiv · 1903.07425

Kobayashi-Hitchin correspondence of generalized holomorphic vector bundles over generalized Kahler manifolds of symplectic type

Ryushi Goto
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Abstract

In the previous paper \cite{Goto_2017}, 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 $\psi$-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 $\psi$-stable Poisson modules over complex surfaces which are not stable in the ordinary sense.

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Ryushi Goto. 2019-03-18. Kobayashi-Hitchin correspondence of generalized holomorphic vector bundles over generalized Kahler manifolds of symplectic type. https://arxiv.org/abs/1903.07425

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