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.

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

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.

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…

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, …

Proves correspondence between harmonic and Higgs bundles.

Study periodic monopoles via algebraic difference modules.

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…

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

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

Study of twisted Kapustin-Witten equations on Riemann surfaces.

Paper proves bijection of periodic instantons to singular monopoles.

Study real structures and $\mathrm{Pin}^-(2)$-monopoles in symplectic and Kähler manifolds.

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

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

Proves existence of Hermitian-Einstein metrics on stable bundles.

The paper establishes a correspondence between solutions of extended Bogomolny equations and Higgs bundles.

Introduces a new equation for complex surfaces, proving stability and inequalities.

Paper solves Hermitian-Einstein equations on noncompact manifolds.

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

Develops correspondence for Bogomolny equations with specific boundary conditions.

Study local perturbations of vector bundles with polynomial curvature solutions.

The paper studies the moduli space of Higgs pairs and their geometric properties.

Reproves results on spherical metrics using parabolic bundles.

This article is an expanded version of talks given by the authors in Oberwolfach, Bochum, and at the Fano Conference in Torino. Some new results (e. g. the material concerning flag varieties, Quot spaces over $¶^1$, and the generalized quiver representations) were included. The main goal is the construction of gauge th…

Established a correspondence between Higgs bundles and Bogomolny equations.

Study of monopoles and q-difference modules correspondence.

We establish the correspondence between tame harmonic bundles and $μ_L$-stable parabolic Higgs bundles with trivial characteristic numbers. We also show the Bogomolov-Gieseker type inequality for $μ_L$-stable parabolic Higgs bundles. Then we show that any local system on a smooth quasi projective variety can be deforme…

We introduce the concept of Spin^G-structure in a SO-bundle, where $G\subset U(V)$ is a compact Lie group containing $-id_V$. We study and classify $Spin^G(4)$-structures on 4-manifolds, we introduce the G-Monopole equations associated with a $Spin^G$-structure. On Kaehler surfaces a Kobayashi-Hitchin correspondence ca…

Monads link instantons and bow solutions in complex geometry.

Study moduli spaces of solutions to Bogomolny equations on surfaces.

Paper defines new stability and metrics for complex spaces.

We study the following question: Let $(X,g)$ be a compact Gauduchon surface, $(E,h)$ be a differentiable rank $r$ vector bundle on $X$, ${\mathcal{D}}$ be a fixed holomorphic structure on $D:=\det(E)$ and $a$ be the Chern connection of the pair $(\mathcal{D},\det(h))$. Does the complex space structure on ${\mathcal{M}}…

We study a certain type of wild harmonic bundles in relation with a Toda equation. We explain how to obtain a classification of the real valued solutions of the Toda equation in terms of their parabolic weights, from the viewpoint of the Kobayashi-Hitchin correspondence. Then, we study the associated integrable variati…

In general, a Kobayashi-Hitchin correspondence establishes an isomorphism between a moduli space of stable algebraic geometric objects and a moduli space of solutions of a certain (generalized) Hermite-Einstein equation. We believe that, for a large class of moduli problems, this correspondence respects the virtual fun…

Paper solves vortex equations on complex surfaces, linking to Higgs bundle stability.

The paper proves estimates for vortex-type equations on compact Riemann surfaces.

We prove that any class $VII$ surface with $b_2=1$ has curves. This implies the "Global Spherical Shell conjecture" in the case $b_2=1$: Any minimal class $VII$ surface with $b_2=1$ admits a global spherical shell, hence it is isomorphic to one of the surfaces in the known list. The main idea of the proof is to show th…

The paper establishes a correspondence between Higgs torsors and connections on curves.

The paper studies obstructions to solutions of the Wess-Zumino-Witten equation and its generalizations.

The paper studies connections on stable bundles and their continuity under metric variations.

Paper generalizes Mochizuki's theorem to stable λ-flat bundles and explores applications to moduli spaces.

The symplectic vortex equations admit a variational description as global minimum of the Yang-Mills-Higgs functional. We study its negative gradient flow on holomorphic pairs $(A,u)$ where $A$ is a connection on a principal $G$-bundle $P$ over a closed Riemann surface $Σ$ and $u: P \rightarrow X$ is an equivariant map …