Related papers: Higgs bundles for the Lorentz group

This paper concerns the relationship between locally homogeneous geometric structures on topological surfaces and the moduli of polystable Higgs bundles on Riemann surfaces, due to Hitchin and Simpson. In particular we discuss the…

By studying the Higgs bundle equations with the gauge group replaced by the group of symplectic diffeomorphisms of the 2-sphere we encounter the notion of a folded hyperkaehler 4-manifold and conjecture the existence of a family of such…

On a complex manifold, a co-Higgs bundle is a holomorphic vector bundle with an endomorphism twisted by the tangent bundle. The notion of generalized holomorphic bundle in Hitchin's generalized geometry coincides with that of co-Higgs…

The cotangent bundle $T^*X$ of a smooth intersection $X$ of two quadrics admits a Lagrangian fibration determined by the intrinsic geometry of $X$. We show that this fibration is actually the Hitchin morphism if we endow $X$ with a…

For any almost-simple group $G$ over an algebraically closed field $k$ of characteristic zero, we describe the automorphism group of the moduli space of semistable $G$-bundles over a connected smooth projective curve $C$ of genus at least…

Abstract. Let G be a complex reductive group and A be an Abelian variety of dimension d over $\mathbb{C}$. We determine the Poincar\'e polynomials and also the mixed Hodge polynomials of the moduli space $\mathcal{M}_{A}^{H}(G)$ of G-Higgs…

Applying the technique of $p$-adic integration, we prove the topological mirror symmetry conjecture of Hausel-Thaddeus for the moduli spaces of (strongly) parabolic Higgs bundles for the structure groups $\text{SL}_n$ and $\text{PGL}_n$,…

We give a birational description of the reduced schemes underlying the irreducible components of the nilpotent cone and the $\CC^\times$-fixed point locus of length two in the moduli space of Higgs bundles. Using these results, we prove…

We study the asymptotic behavior of Hitchin's hyperk\"ahler metric on the moduli space of rank two irregular Higgs bundles over $\mathbb{C}P^1$. Along a generic curve, we prove that the Hitchin metric is asymptotic to the semiflat metric at…

We study the hyperk\"ahler analogues of moduli spaces of semistable n-gons in complex projective space. We prove that the hyperk\"ahler Kirwan map is surjective and produce a formula that recursively calculates the Betti numbers of these…

This article is based in part on lecture notes prepared for the summer school "The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles" at the Institute for Mathematical Sciences at the National University of Singapore in July…

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…

In gauge theories, observable quantities have to be gauge-invariant. In general, this requires composite operators, which usually have substantially different properties, e.g. masses, than the elementary particles. Theories with a Higgs…

In this paper, we derive a maximum principle for a type of elliptic systems and apply it to analyze the Hitchin equation for cyclic Higgs bundles. We show several domination results on the pullback metric of the (possibly branched) minimal…

Following the strategy outlined in [DP09] arXiv:math/0604617 and [DP22] arXiv:math/0604617 for bundles of rank 2 on a smooth projective curve of genus $2$, we construct flat connections over the moduli of stable bundles, with singularities…

We give an algebraic geometric compactification of certain moduli spaces of semistable E-pairs in the sense of Yokogawa. In particular, we obtain a compactification of the moduli spaces of semistable Higgs pairs on a curve which were…

Given a compact Riemann surface $\Sigma$ of genus $g_\Sigma\, \geq\, 2$, and an effective divisor $D\, =\, \sum_i n_i x_i$ on $\Sigma$ with $\text{degree}(D)\, <\, 2(g_\Sigma -1)$, there is a unique cone metric on $\Sigma$ of constant…

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…

We provide a construction of the moduli spaces of framed Hitchin pairs and their master spaces. These objects have come to interest as algebraic versions of solutions of certain coupled vortex equations by work of Lin and Stupariu. Our…

We develop a systematic method to describe the moduli space of vacua of four dimensional $\mathcal{N}=2$ class ${\cal S}$ theories including Coulomb branch, Higgs branch and mixed branches. In particular, we determine the Higgs and mixed…