Related papers: On vanishing theorems for Higgs bundles

We investigate principal $G$-bundles on a compact K\"ahler manifold, where $G$ is a complex algebraic group such that the connected component of it containing the identity element is reductive. Defining (semi)stability of such bundles, it…

Let $(E,\Phi)\rightarrow (X,\omega_X)$ be a Higgs bundle over a compact K\"ahler manifold. We suppose that the holomorphic vector bundle $E$ decomposes into a direct sum of holomorphic line bundles. In this paper, we give the necessary and…

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…

Relying on a notion of "numerical effectiveness" for Higgs bundles, we show that the category of "numerically flat" Higgs vector bundles on a smooth projective variety $X$ is a Tannakian category. We introduce the associated group scheme,…

In this paper we generalize the theory of multiplicative $G$-Higgs bundles over a curve to pairs $(G,\theta)$, where $G$ is a reductive algebraic group and $\theta$ is an involution of $G$. This generalization involves the notion of a…

The purpose of this paper is to extend the Donaldson-Corlette theorem to the case of vector bundles over cell complexes. We define the notion of a vector bundle and a Higgs bundle over a complex, and describe the associated Betti, de Rham…

M-theory compactified on $G_2$-holonomy manifolds results in 4d $\mathcal{N}=1$ supersymmetric gauge theories coupled to gravity. In this paper we focus on the gauge sector of such compactifications by studying the Higgs bundle obtained…

In this paper we consider a canonical compactification of Hitchin's moduli space of stable Higgs bundles with fixed determinant of odd degree over a Riemann surface, producing a projective variety by gluing in a divisor at infinity. We give…

On a Riemannian manifold of dimension $n$ we extend the known analytic results on Yang-Mills connections to the class of connections called $\Omega$-Yang-Mills connections, where $\Omega$ is a smooth, not necessarily closed, $(n-4)$-form.…

We introduce the notion of $T$-stability for torsion-free Higgs sheaves as a natural generalization of the notion of $T$-stability for torsion-free coherent sheaves over compact complex manifolds. We prove similar properties to the…

We show that a unipotent vector bundle on a non-Kaehler compact complex manifold does not admit a flat holomorphic connection in general. We also construct examples of topologically trivial stable vector bundle on compact Gauduchon manifold…

Let $X$ be a compact Gauduchon manifold, and let $E$ and $V_0$ be holomorphic vector bundles over $X$. Suppose that $E$ is stable when considering all subsheaves preserved by a Higgs field $\theta\in H^0($End$(E)\otimes V_0)$. Then a…

This thesis contains work which appeared in several papers. Additionally to the results in the papers it contains a detailed introduction and some further proofs and remarks. The dissertation gives a description of the topology and…

In this paper, we consider the gradient flow of the Yang-Mills-Higgs functional for Higgs pairs on a Hermitian vector bundle $(E, H_{0})$ over a compact K\"ahler manifold $(M, \omega )$. We study the asymptotic behavior of the…

In this paper we study the relation between parabolic Higgs bundles and irreducible representations of the fundamental group of punctured Riemann surfaces established by Simpson. We generalize a result of Hitchin, identifying those…

We establish an isomorphism of complex $K$-theory of the moduli space $\check{\mathcal{M}}$ of $``SL_n"$-Higgs bundles of degree $d$ and rank $n$ (in the sense of Hausel--Thaddeus) and twisted complex $K$-theory of the orbifold…

We construct a universal partial compactification of the relative moduli space of semistable meromorphic Higgs bundles over the stack of stable pointed curves. It parametrizes meromorphic Gieseker Higgs bundles, and is equipped with a flat…

In a recent work, Kai Tang conjectured that any compact Hermitian manifold with non-zero constant mixed curvature must be K\"ahler. He confirmed the conjecture in complex dimension $2$ and for Chern K\"ahler-like manifolds in general…

Using the $L^2$ norm of the Higgs field as a Morse function, we study the moduli spaces of $U(p,q)$-Higgs bundles over a Riemann surface. We require that the genus of the surface be at least two, but place no constraints on $(p,q)$. A key…

We provide an algebraic framework for quantization of Hermitian metrics that are solutions of the Hitchin equation for Higgs bundles over a projective manifold. Using Geometric Invariant Theory, we introduce a notion of balanced metrics in…