Related papers: Global properties of Higgs bundle moduli spaces

This paper concerns the moduli spaces of rank two parabolic Higgs bundles and parabolic K(D) pairs over a smooth curve. Precisely which parabolic bundles occur in stable K(D), pairs and stable Higgs bundles is determined. Using Morse…

Holomorphic principal G-bundles over a complex manifold M can be studied using non-abelian cohomology groups H^1(M,G). On the other hand, if M=\Sigma is a closed Riemann surface, there is a correspondence between holomorphic principal…

We present a review of bundle gerbes, emphasizing their relations to Lie groups. Indeed, compact Lie groups do not only carry the structure of a Riemannian manifold, but also canonical families of bundle gerbes. We recall the construction…

We construct a Petersson-Weil type K\"ahler form on the moduli spaces of Higgs bundles over a compact K\"ahler manifold. A fiber integral formula for this form is proved, from which it follows that the Petersson-Weil form is the curvature…

In this paper we show that the dimensionally reduced Seiberg-Witten equations lead to a Higgs field and study the resulting moduli spaces. The moduli space arising out of a subset of the equations, shown to be non-empty for a compact…

Let $X$ be a compact Riemann surface of genus $g \geq 2$, and let $D \subset X$ be a fixed finite subset. Let $\mathcal{M}(r,d,\alpha)$ denote the moduli space of stable parabolic $G$-bundles (where $G$ is a complex orthogonal or symplectic…

We consider canonical symplectic structure on the moduli space of flat ${\g}$-connections on a Riemann surface of genus $g$ with $n$ marked points. For ${\g}$ being a semisimple Lie algebra we obtain an explicit efficient formula for this…

Let $G$ be a Lie group, with an invariant non-degenerate symmetric bilinear form on its Lie algebra, let $\pi$ be the fundamental group of an orientable (real) surface $M$ with a finite number of punctures, and let $\bold C$ be a family of…

Let $X$ be a compact connected Riemann surface of genus $g \geq 2$ and $G$ a connected reductive affine algebraic group over $\mathbb{C}$. We prove the semiprojectivity of the moduli spaces of semistable $G$-Higgs bundles and $G$-bundles…

Higgs bundles and non-abelian Hodge theory provide holomorphic methods with which to study the moduli spaces of surface group representations in a reductive Lie group G. In this paper we survey the case in which G is the isometry group of a…

In this paper we investigate the moduli space of parabolic Higgs bundles over a punctured Riemann surface with varying weights at the punctures. We show that the harmonic metric depends analytically on the weights and the stable Higgs…

We present a systematic study of involutions on the moduli space of $G$-Higgs bundles over an elliptic curve $X$, where $G$ is complex reductive affine algebraic group. The fixed point loci in the moduli space of $G$-Higgs bundles on $X$,…

Montonen-Olive duality implies that the categories of A-branes on the moduli spaces of Higgs bundles on a Riemann surface C for a pair of Langlands-dual groups are equivalent. We reformulate this as a statement about categories of B-branes…

In previous papers we introduced the notion of special Bohr - Sommerfeld lagrangian cycles on a compact simply connected symplectic manifold with integer symplectic form, and presented the main interesting case: compact simply connected…

In this paper we construct certain moduli spaces, which we call moduli spaces of (principal) $F$-bundles, and study their basic properties. These spaces are associated to triples consisting of a smooth projective geometrically connected…

We consider the moduli space ${\cal M}(G)$ of $G$-Higgs bundles over a compact Riemann surface $X$, where $G$ is a semisimple complex Lie group, and study the action of a finite group $\Gamma$ on ${\cal M}(G)$ induced by a holomorphic…

The Betti numbers of moduli spaces of representations of a universal central extension of a surface group in the groups U(2,1) and SU(2,1) are calculated. The results are obtained using the identification of these moduli spaces with moduli…

We find an agreement of equivariant indices of semi-classical homomorphisms between pairwise mirror branes in the GL(2) Higgs moduli space on a Riemann surface. On one side we have the components of the Lagrangian brane of U(1,1) Higgs…

We shall construct a natural Higgs bundle structure on the complexified K\"ahler cone of a compact K\"ahler manifold, which can be seen as an analogy of the classical Higgs bundle structure associated to a variation of Hodge structure. In…

This is a review article exploring similarities between moduli of quiver representations and moduli of vector bundles over a smooth projective curve. After describing the basic properties of these moduli problems and constructions of their…