arXiv research

Study Kobayashi-Hitchin correspondence for special sheaves on Kähler manifolds.

Paper extends Kobayashi-Hitchin correspondence to non-Kähler manifolds.

The Kobayashi-Hitchin correspondence is proven for twisted vector bundles on Kähler manifolds.

Establishes Kobayashi-Hitchin correspondence for nef and big classes.

Paper describes integrable structure of Hitchin moduli spaces.

Generalizes Higgs bundles theory using a vector bundle twist.

The Kobayashi-Hitchin correspondence is established for mini-holomorphic bundles on certain 3-folds.

In this paper we develop a Kobayashi-Hitchin type correspondence between solutions of the extended Bogomolny equations on $Σ\times \RP$ with Nahm pole singularity at $Σ\times \{0\}$ and the Hitchin component of the stable $SL(2,\mathbb{R})$ Higgs bundle; this verifies a conjecture of Gaiotto and Witten. We also develop…

Study of energy functional on Deligne-Hitchin moduli space sections.

The paper establishes a correspondence for quiver bundles over generalized Kähler manifolds.

Study asymptotics of hyperkähler geometry on singular fibers of Hitchin moduli space.

We establish a Kobayashi-Hitchin correspondence for the stable Higgs sheaves on a compact Kaehler manifold. Using it, we also obtain a Kobayashi-Hitchin correspondence for the stable Higgs G-sheaves, where G is any complex reductive linear algebraic group.

Study proves correspondence for special bundles on complex surfaces.

Paper studies compactifications of Higgs bundles and self-duality equations.

We extend the Donaldson-Corlette-Hitchin-Simpson correspondence between Higgs bundles and flat connections on compact Kähler manifolds to compact quasi-regular Sasakian manifolds. A particular consequence is the translation of restrictions on Kähler groups proved using the Donaldson-Corlette-Hitchin-Simpson corresponde…

Proves correspondence between harmonic and Higgs bundles.

This paper proves Hitchin moduli spaces are ALG gravitational instantons.

Let $X$ be a smooth projective complex variety with an ample line bundle $L$, and let $D$ be a simple normal crossing divisor. We establish the Kobayashi-Hitchin correspondence between tame harmonic bundles on $X-D$ and $μ_L$-stable parabolic $λ$-flat bundles with trivial characteristic numbers on $(X,D)$. Especially, …

A simple trick invoking objective B-fields is employed to refine the concept of characteristic classes for twisted bundles. Then the objective stability and objective Einstein metrics are introduced and a new Hitchin-Kobayashi correspondence is established between them. As an application the SO(3)-instanton moduli spac…

We prove a very general Kobayashi-Hitchin correspondence on arbitrary compact Hermitian manifolds. This correspondence refers to moduli spaces of "universal holomorphic oriented pairs". Most of the classical moduli problems in complex geometry (e. g. holomorphic bundles with reductive structure groups, holomorphic pair…

The paper studies properties of triangle and shearing invariants in PSL(n,R) and connects them to a slice of Hitchin components.

Study of monopoles and q-difference modules correspondence.

Study on $GL(1|1)$ Higgs bundles over Riemann surfaces.

This paper establishes a correspondence between Einstein-Hermitian metrics and stability for generalized holomorphic vector bundles over symplectic type generalized Kahler manifolds.

Investigates nearly Kähler and parallel G2 manifolds using Hitchin functionals.

By referring to theorems of Donaldson and Hitchin, we exhibit a rigorous AdS/CFT-type correspondence between classical 2+1 dimensional vacuum general relativity theory on S x R and SO(3) Hitchin theory (regarded as a classical conformal field theory) on the spacelike past boundary S, a compact, oriented Riemann surface…

Numerical experiments support conjecture about opers and nonabelian Hodge.

In this paper, we introduce the notions of $α$-Hermitian-Einstein metric and $α$-stability for $I_\pm$-holomorphic vector bundles on bi-Hermitian manifolds. Moreover, we establish a Kobayashi-Hitchin correspondence for $I_\pm$-holomorphic vector bundles on bi-Hermitian manifolds. Examples of such vector bundles include…

We prove that given a Hitchin representation in a real split rank 2 group $\mathsf G_0$, there exists a unique equivariant minimal surface in the corresponding symmetric space. As a corollary, we obtain a parametrization of the Hitchin components by a Hermitian bundle over Teichmüller space. The proof goes through intr…

Study extended Bogomolny equations on curved space with special boundary conditions.

Study on Higgs bundles and hyperpolygon spaces using Hitchin metrics.

Study the geometry of twistor spaces with rotating circle action.

Study of twisted Kapustin-Witten equations on Riemann surfaces.

A twisted Higgs bundle on a Kähler manifold $X$ is a pair $(E,φ)$ consisting of a holomorphic vector bundle $E$ and a holomorphic bundle morphism $φ\colon M\otimes E \to E$ for some holomorphic vector bundle $M$. Such objects were first considered by Hitchin when $X$ is a curve and $M$ is the tangent bundle of $X$, and…

We develop a complete Hitchin-Kobayashi correspondence for twisted pairs on a compact Riemann surface X. The main novelty lies in a careful study of the the notion of polystability for pairs, required for having a bijective correspondence between solutions to the Hermite-Einstein equations, on one hand, and polystable …

Let $(S,g_0)$ be a hyperbolic surface, $ρ$ be a Hitchin representation for $PSL(n,\mathbb R)$, and $f$ be the unique $ρ$-equivariant harmonic map from $(\widetilde S, \widetilde g_0)$ to the corresponding symmetric space. We show its energy density satisfies $e(f)\geq 1$ and equality holds at one point only if $e(f)\eq…

In 1992, Hitchin used his theory of Higgs bundles to construct an important family of representations of the fundamental group of a closed, oriented surface of genus at least two into the split real form of a complex adjoint simple Lie group. These Hitchin representations comprise a component of the space of conjugacy …

Paper proves Hermitian-Yang-Mills metrics for stable Kähler bundles.

We define Hitchin's moduli space for a principal bundle $P$, whose structure group is a compact semisimple Lie group $K$, over a compact non-orientable Riemannian manifold $M$. We use the Donaldson-Corlette correspondence, which identifies Hitchin's moduli space with the moduli space of flat $K^\mathbb{C}$-connections,…

Study describes moduli spaces of flat bundles on Sasakian manifolds.

Geometric methods for surface group representations in higher rank SL(2m+1,R).

The paper explores Higgs bundles and their moduli spaces on Riemann surfaces.

Study on compact Quasi-Einstein manifolds yields diameter estimates and Hitchin-Thorpe inequality conditions.

We present a sigma model field theoretic realization of Hitchin's generalized complex geometry, which recently has been shown to be relevant in compactifications of superstring theory with fluxes. Hitchin sigma model is closely related to the well known Poisson sigma model, of which it has the same field content. The c…

Conditions for polyhedral Kähler metrics on CP^n with specific singularities.

For a closed surface S, the Hitchin component Hit_n(S) is a preferred component of the character variety consisting of group homomorphisms from the fundamental group pi_1(S) to the Lie group PSL_n(R). We construct a parametrization of the Hitchin component that is well-adapted to a maximal geodesic lamination on the su…

The study describes the geometry of surfaces and their representations in SL(3,R).

New equivalence found for flat vector bundles without extra conditions.