Related papers: Constructing co-Higgs bundles on CP^2

In this paper we give a gauge theoretic construction of the joint moduli space of stable G-Higgs bundles on closed Riemann surfaces, where the Riemann surface structure is allowed to vary in the Teichm\"uller space of the underlying smooth…

A hermitian Higgs bundle is a triple $({\mathfrak E},h) = (E,\Phi, h)$, where ${\mathfrak E}=(E,\Phi)$ is a Higgs bundle and $(E,h)$ is a holomorphic hermitian vector bundle. It is well-known that several results on holomorphic vector…

We define homogeneous principal Higgs and co-Higgs bundles over irreducible Hermitian symmetric spaces of compact type. We provide a classification for each type of object up to isomorphism, which in each case can be interpreted as defining…

We define the isomonodromic deformation of a Higgs bundle over a compact Riemann surface via the Hitchin-Simpson correspondence and the isomonodromic deformation of a local system. This deformation defines a real analytic section of the…

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…

We give a geometric characterisation of the topological invariants associated to SO(m,m+1)-Higgs bundles through KO-theory and the Langlands correspondence between orthogonal and symplectic Hitchin systems. By defining the split orthogonal…

We study the algebraic geometry of twisted Higgs bundles of cyclic type along complex curves. These objects, which generalize ordinary cyclic Higgs bundles, can be identified with representations of a cyclic quiver in a twisted category of…

We examine several classes of manifolds which have the same cohomology ring as an Eschenburg space (a family of biquotients which is a main source of manifolds with positive curvature). One family are the 3-sphere bundles over CP^2. Another…

We characterize those unipotent representations of the fundamental group $\pi_1(X,x)$ of a compact Kaehler manifold $X$, which correspond to a Higgs bundle whose underlying Higgs field is equal to zero. The characterization is parallel to…

We consider the moduli space of stable parabolic Higgs bundles of rank $r$ and fixed determinant, and having full flag quasi-parabolic structures over an arbitrary parabolic divisor on a smooth complex projective curve $X$ of genus $g$,…

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 smooth projective curve over a field of characteristic p>0. We show that the Hitchin morphism, which associates to a Higgs bundle its characteristic polynomial, has a non-trivial deformation over the affine line. This deformation…

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…

This survey provides an introduction to basic questions and techniques surrounding the topology of the moduli space of stable Higgs bundles on a Riemann surface. Through examples, we demonstrate how the structure of the cohomology ring of…

Let $C$ be a smooth projective curve of genus $2$. Following a method by O' Grady, we construct a semismall desingularization $\tilde{\mathcal{M}}_{Dol}^G$ of the moduli space $\mathcal{M}_{Dol}^G$ of semistable $G$-Higgs bundles of degree…

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…

Let $M$ be a compact complex manifold equipped with a Gauduchon metric. If $TM$ is holomorphically trivial, and (V, \theta) is a stable SL(r,{\mathbb C})-Higgs bundle on $M$, then we show that $\theta= 0$. We show that the correspondence…

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…

We define a Fourier-Mukai transform for Higgs bundles on smooth curves and study its properties. It is shown that the transform of a stable zero-degree Higgs bundle is an algebraic vector bundle on the cotangent bundle of the Jacobian of…

Let X be a compact connected Riemann surface of genus g > 0 equipped with a nonzero holomorphic 1-form. Let M denote the moduli space of semistable Higgs bundles on X of rank r and degree r(g-1)+1; it is a complex symplectic manifold. Using…