Related papers: Global properties of Higgs bundle moduli spaces

We introduce a notion of quasi-antisymmetric Higgs $G$-bundles over curves with marked points. They are endowed with additional structures, which replace the parabolic structures at marked points in the parabolic Higgs bundles. The latter…

We extend Hitchin's results on "The self-duality equations on a Riemann surface" (Proc. LMS (3), vol. 55, 1987) to orbifold Riemann surfaces. We prove existence results for orbifold solutions of the Yang-Mills-Higgs equations and construct…

Let $X$ be a compact Riemann surface $X$ of genus $\geqslant 2$ and let $\sigma:X \to X$ be an anti-holomorphic involution. Using real and quaternionic systems of Hodge bundles, we study the topology of the real locus $\mathbb{R}…

We count the connected components in the moduli space of PU(p,q)-representations of the fundamental group for a closed oriented surface. The components are labelled by pairs of integers which arise as topological invariants of the flat…

We calculate the characteristic classes for flat SL(n,R) and Sp(2m,R)-bundles over a compact surface as functions of the spectral data in the Higgs bundle description, which consists of the points of order 2 in an abelian variety. Using…

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…

Higgs fields are attributes of classical gauge theory on a principal bundle $P\to X$ whose structure Lie group $G$ if is reducible to a closed subgroup $H$. They are represented by sections of the quotient bundle $P/H\to X$. A problem lies…

Higgs bundles appeared a few decades ago as solutions to certain equations from physics and have attracted much attention in geometry as well as other areas of mathematics and physics. Here, we take a very informal stroll through some…

Through the action of anti-holomorphic involutions on a compact Riemann surface, we construct families of (A,B,A)-branes in the moduli spaces of G_c-Higgs bundles on the Riemann surface. We study the geometry of these (A,B,A)-branes in…

We place the representation variety in the broader context of abelian and nonabelian cohomology. We outline the equivalent constructions of the moduli spaces of flat bundles, of smooth integrable connections, and of holomorphic integrable…

On a compact connected Riemann surface $C$ of genus at least $2$, we construct Lagrangian correspondences between moduli spaces of rank-$n$ Higgs bundles (respectively, holomorphic connections) and the Hilbert schemes of points on $T^\ast…

We shall prove that a moduli space of flat irreducible Lie algebroid connections over a compact manifold has locally a natural structure of a smooth differentiable space. This is a generalization of some well known results for the moduli…

We generalize the construction of M. Lieblich for the compactification of the moduli stack of $\PGL_r$-bundles on algebraic spaces to the moduli stack of Tanaka-Thomas $\PGL_r$-Higgs bundles on algebraic schemes. The method we use is the…

We introduce the notion of generalized hyperpolygon, which arises as a representation, in the sense of Nakajima, of a comet-shaped quiver. We identify these representations with rigid geometric figures, namely pairs of polygons: one in the…

The character varieties of representations of a surface group into the Lie groups SL(m,H), SO(2m,H) and Sp(m,m) have a holomorphic description in terms of the moduli space of Higgs bundles. We show that the fibres of the integrable system…

In this paper, we study Hermitian-Yang-Mills connections (HYM) on a smooth Hermitian vector bundle over compact K\"{a}hler manifold. We calculate the virtual dimension of the moduli space of HYM connections and provide an analytic proof…

Mid-dimensional $(A,B,A)$ and $(B,B,B)$-branes in the moduli space of flat $G_{\mathbb C}$-connections appearing from finite group actions on compact Riemann surfaces are studied. The geometry and topology of these spaces is then described…

We study moduli spaces of Higgs bundles with two poles on an elliptic curve. We describe all singular fibers of the Hitchin map, including the nilpotent cone. To achieve this, we consider a modular map that lifts Higgs bundles with five…

In this paper we continue our study on the moduli spaces of flat G-bundles, for any semi-simple Lie group G, over a Riemann surface by using heat kernel and Reidemeister torsion. Formulas for intersection numbers on the moduli spaces over a…

We study the moduli spaces of flat SL(r)- and PGL(r)-connections, or equivalently, Higgs bundles, on an algebraic curve. These spaces are noncompact Calabi-Yau orbifolds; we show that they can be regarded as mirror partners in two different…