Related papers: Kobayashi-Hitchin correspondence for tame harmonic…

We establish the correspondence between tame harmonic bundles and $\mu_L$-stable parabolic Higgs bundles with trivial characteristic numbers. We also show the Bogomolov-Gieseker type inequality for $\mu_L$-stable parabolic Higgs bundles.…

We prove the Kobayashi-Hitchin correspondence between good wild harmonic bundles and polystable good filtered $\lambda$-flat bundles satisfying a vanishing condition. We also study the correspondence for good wild harmonic bundles with the…

The Corlette-Donaldson-Hitchin-Simpson's correspondence states that, on a compact K\"ahler manifold $(X, \omega )$, there is a one-to-one correspondence between the moduli space of semisimple flat complex vector bundles and the moduli space…

We prove the Kobayashi-Hitchin correspondence for parabolic bundles over compact nonK\"{a}hler surfaces with simple normal crossing divisor or compact nonK\"{a}hler manifolds of any dimension with smooth divisor.

We extend the Donaldson-Corlette-Hitchin-Simpson correspondence between Higgs bundles and flat connections on compact K\"ahler manifolds to compact quasi-regular Sasakian manifolds. A particular consequence is the translation of…

In this paper, we establish the Hitchin--Kobayashi correspondence for the $I_\pm$-holomorphic quiver bundle $\mathcal{E}=(E,\phi)$ over a compact generalized K\"{a}hler manifold $(X, I_+,I_-,g, b)$ such that $g$ is Gauduchon with respect to…

A twisted quiver bundle is a set of holomorphic vector bundles over a complex manifold, labelled by the vertices of a quiver, linked by a set of morphisms twisted by a fixed collection of holomorphic vector bundles, labelled by the arrows.…

Given a flat vector bundle over a compact Riemannian manifold, Corlette and Donaldson proved that it admits harmonic metrics if and only if it is semi-simple. In this paper, we extend this equivalence to arbitrary vector bundles without any…

The notion of flat $\lambda$-connections as the interpolation of usual flat connections and Higgs fields was suggested by Deligne and further studied by Simpson. Mochizuki established the Kobayashi--Hitchin-type theorem for $\lambda$-flat…

We prove the Kobayashi-Hitchin correspondence and the approximate Kobayashi-Hitchin correspondence for twisted holomorphic vector bundles on compact K\"ahler manifolds. More precisely, if $X$ is a compact manifold and $g$ is a Gauduchon…

We develop a complete Hitchin-Kobayashi correspondence for twisted pairs on a compact Riemann surface X. The main novelty lies in a careful study of the the notion of polystability for pairs, required for having a bijective correspondence…

We prove a Hitchin-Kobayashi correspondence for extensions of Higgs bundles. The results generalize known results for extensions of holomorphic bundles. Using Simpson's methods, we construct moduli spaces of stable objects. In an appendix…

The so-called Hitchin-Kobayashi correspondence, proved by Donaldson, Uhlenbeck and Yau, establishes that an indecomposable holomorphic vector bundle over a compact Kahler manifold admits a Hermitian-Einstein metric if and only if the bundle…

In this paper, we introduce the notions of $\alpha$-Hermitian-Einstein metric and $\alpha$-stability for $I_\pm$-holomorphic vector bundles on bi-Hermitian manifolds. Moreover, we establish a Kobayashi-Hitchin correspondence for…

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…

Let $M$ be a quasi-regular compact connected Sasakian manifold, and let $N = M/S^1$ be the base projective variety. We establish an equivalence between the class of Sasakian $G$-Higgs bundles over $M$ and the class of parabolic (or…

Let $X$ be a compact Riemann surface and $\mathbb{P}^1$ be the complex projective line. In this paper, we introduce an equation which we call the doubly-coupled vortex equation on $X$. We show that the existence of a solution of the…

Let $E$ be a holomorphic vector bundle. Let $\theta$ be a Higgs field, that is a holomorphic section of $End(E)\otimes\Omega^{1,0}_X$ satisfying $\theta^2=0$. Let $h$ be a pluriharmonic metric of the Higgs bundle $(E,\theta)$. The tuple…

In this continuation of \cite{BK} we investigate the non-abelian Hodge correspondence on compact Sasakian manifolds with emphasis on the quasi-regular case. On quasi-regular Sasakian manifolds, we introduce the notions of quasi-regularity…

In this paper, we consider a generalization of the theory of Higgs bundles over a smooth complex projective curve in which the twisting of the Higgs field by the canonical bundle of the curve is replaced by a rank 2 vector bundle. We define…