Related papers: A Brief Survey of Higgs Bundles

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…

Hitchin in [Duke Math. J. 54 (1), 91-114 (1987)] introduced a proper morphism from the moduli space of stable $G$-Higgs bundles ($G=\mathrm{GL}(n,\mathbb{C}),\mathrm{Sp}(2m,\mathbb{C})$ and $\mathrm{SO}(n,\mathbb{C})$) over a curve to a…

This brief survey aims to set the stage and summarize some of the ideas under discussion at the Workshop on Singular Geometry and Higgs Bundles in String Theory, to be held at the American Institute of Mathematics from October 30th to…

Let T be the one-dimensional complex torus. We consider the action of an automorphism of a Riemann surface X on the cohomology of the T-equivariant determinant line bundle over the moduli space of rank two Higgs bundles on X with fixed…

Given an holomorphic Higgs bundle on a compact Riemann surface of genus greater than one, we construct a DQ-module supported by the spectral curve associated to this bundle. Then, we relate quantum curves arising in various situations…

We establish a gluing construction for Higgs bundles over a connected sum of Riemann surfaces in terms of solutions to the $\text{Sp(4}\text{,}\mathbb{R}\text{)}$-Hitchin equations using the linearization of a relevant elliptic operator.…

We study the moduli space of Higgs bundles on a compact Riemann surface. It was shown by Thaddeus and Hausel (in rank 2) and Markman (in general rank) that the rational cohomology ring of this space is generated by universal classes. In…

By virtue of the well-known theorem, a structure Lie group G of a principal bundle P is reducible to its closed subgroup H iff there exists a global section of the quotient bundle P/H. In gauge theory, such sections are treated as classical…

We introduce the notion of Hermitian Higgs bundle as a natural generalization of the notion of Hermitian vector bundle and we study some vanishing theorems concerning Hermitian Higgs bundles when the base manifold is a compact complex…

Parabolic triples of the form $(E_*,\theta,\sigma)$ are considered, where $(E_*,\theta)$ is a parabolic Higgs bundle on a given compact Riemann surface $X$ with parabolic structure on a fixed divisor $S$, and $\sigma$ is a nonzero section…

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 step is…

We introduce para-complex and pseudo-Riemannian geometric methods for the study of representations of surface groups in $\mathrm{SL}(2m+1,\mathbb{R})$. For $m=1$ our techniques allow to recover several known results for Hitchin…

We study the hypersymplectic geometry of the moduli space of solutions to Hitchin's harmonic map equations on a $G$-bundle. This is the split-signature analogue of Hitchin's Higgs bundle moduli space. Due to the lack of definiteness, this…

Given a compact Riemann surface $X$ and a semisimple affine algebraic group $G$ defined over $\mathbb C$, there are moduli spaces of Higgs bundles and of connections associated to $(X,\, G)$. We compute the Brauer group of the smooth locus…

For a semisimple real Lie group $G$, we study topological properties of moduli spaces of polystable parabolic $G$-Higgs bundles over a Riemann surface with a divisor of finitely many distinct points. For a split real form of a complex…

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…

In this paper we study the geometry of the moduli space of (non-strongly) parabolic Higgs bundles over a Riemann surface with marked points. We show that this space possesses a Poisson structure, extending the one on the dual of an Atiyah…

Holomorphic chains on a Riemann surface arise naturally as fixed points of the natural C*-action on the moduli space of Higgs bundles. In this paper we associate a new quiver bundle to the Hom-complex of two chains, and prove that stability…

Fix a simple complex Lie group G and a principal sl(2,C) subalgebra of Lie(G). Then the moduli space of semi-stable, topologically trivial G-Higgs bundles on a hyperbolic, spin Riemann surface acquires a marked point. This is the unique…

Let $G$ be a complex semisimple Lie group and $\mathfrak g$ its Lie algebra. In this paper, we study a special class of cyclic Higgs bundles constructed from a $\mathbb Z$-grading $\mathfrak g = \bigoplus_{j=1-m}^{m-1}\mathfrak g_j$ by…