Related papers: Dimensional reduction of stable Higgs bundle and t…
Given a vector bundle $E$ on a smooth projective curve or surface $X$ carrying the structure of a $V$-twisted Hitchin pair for some vector bundle $V$, we observe that the associated tautological bundle $E^{[n]}$ on the punctual Hilbert…
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…
By dimensional reduction, Einstein-Hermitian equations of n + 1 dimensional closed Kahler manifolds lead to vortex equations of n dimensional closed Kahler manifolds. A Yang-Mills-Higgs functional to unitary bundles over closed Kahler…
On any complex smooth projective curve with positive genus, we construct Hilbert bundles that admit Hermitian--Einstein metrics. Our main constructive step is by investigating the arithmetic property of the upper half plane in Bridgeland's…
We consider the moduli space of semistable Higgs bundles on a smooth projective curve. Motivated by mirror symmetry, Hausel and Hitchin showed that over an open of the locus of smooth Hitchin fibers, the duality of Donagi-Pantev intertwines…
New solutions to the abelian U(1) Higgs model, corresponding to vortices of integer and half-integer winding number bound onto the edges of domain walls and possibly surrounded by annular current flows, are described, based on a…
We demonstrate the existence and uniqueness of the solution to the Dirichlet problem for a generalization of Hitchin's equation for diagonal harmonic metrics on cyclic Higgs bundles. The generalized equations are formulated using…
The Donaldson-Fujiki K\"ahler reduction of the space of compatible almost complex structures, leading to the interpretation of the scalar curvature of K\"ahler metrics as a moment map, can be lifted canonically to a hyperk\"ahler reduction.…
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…
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…
A holomorphic triple over a compact Riemann surface consists of two holomorphic vector bundles and a holomorphic map between them. After fixing the topological types of the bundles and a real parameter, there exist moduli spaces of stable…
In this article, we establish a Hitchin-Kobayashi type correspondence for generalised Seiberg-Witten monopole equations on Kahler surfaces. We show that the "stability" criterion we obtain, for the existence of solutions, coincides with…
Given a tuple of holomorphic differentials on a Riemann surface, one can define a Higgs bundle in the Hitchin section and a natural symmetric pairing of the Higgs bundle. We study whether a Higgs bundle of rank 3 in the Hitchin section has…
In this paper we consider the topological side of a problem which is the analogue of Sen's S-duality testing conjecture for Hitchin's moduli space of rank 2 stable Higgs bundles of fixed determinant of odd degree over a Riemann surface. We…
We develop a Lie-theoretic perspective on Hitchin's equations for cyclic $G$-Higgs bundles, which we use to study analytic and geometric properties of harmonic maps. Among other things, we prove Dai-Li's conjecture on the monotonicity of…
We generalize the classical theory of Higgs bundles, spectral curves and Norm maps to Deligne-Mumford curves. As an application, under some mild conditions, we prove the Strominger-Yau-Zaslow duality for the moduli spaces of Higgs bundles…
Self-dual vortex solutions are studied in detail in the generalized abelian Higgs model with independent Chern-Simons interaction. For special choices of couplings, it reduces to a Maxwell-Higgs model with two scalar fields, a…
We prove an analogue of the Hitchin-Kobayashi correspondence for compact, oriented, taut Riemannian foliated manifolds with transverse Hermitian structure. In particular, our Hitchin-Kobayashi theorem holds on any compact Sasakian manifold.…
Faltings conjectured that under the p-adic Simpson correspondence, finite dimensional p-adic representations of the geometric \'etale fundamental group of a smooth proper p-adic curve X are equivalent to semi-stable Higgs bundles of degree…
This paper is devoted to the study of the Higgs bundle associated with the universal abelian variety over the good reduction of a Shimura curve of PEL type. Due to the endomorphism structure, the Higgs bundle decomposes into the direct sum…