arXiv research

Study nilpotent Higgs bundles and Calabi-Yau moduli metrics.

Study families of flat connections with nilpotent Higgs fields, showing similar monodromy to regular Higgs bundles.

Study shows unique harmonic metrics for certain Higgs bundles over non-compact surfaces.

Study quadratic one-forms on logarithmic Higgs bundles on pointed curves.

Study very stable Higgs bundles on Riemann surfaces, linking to multiplicity and mirror symmetry.

The Gaiotto locus for Sp(2n) is shown to lie in the nilpotent cone.

For the moduli space of Higgs bundles on a Riemann surface of positive genus, critical points of the natural Morse-Bott function lie along the nilpotent cone of the Hitchin fibration and are representations of $\mbox{A}$-type quivers in a twisted category of holomorphic bundles. The critical points that globally minimi…

Study expanding Ricci solitons on vector bundles, reducing to Higgs bundle equations.

Let $(\mathcal{E}, φ)$ be a rank two co-Higgs vector bundles on a Kähler compact surface $X$ with $φ\in H^0(X,End(\mathcal{E})\otimes T_X)$ nilpotent. If $(\mathcal{E}, φ)$ is semi-stable, then one of the following holds up to finite \' etale cover: $i)$ $X$ is uniruled. $ii)$ $X$ is a torus and $(\mathcal{E}, φ)$ is s…

Let $E$ be a holomorphic vector bundle. Let $θ$ be a Higgs field, that is a holomorphic section of $End(E)\otimesΩ^{1,0}_X$ satisfying $θ^2=0$. Let $h$ be a pluriharmonic metric of the Higgs bundle $(E,θ)$. The tuple $(E,θ,h)$ is called a harmonic bundle. Let $X$ be a complex manifold, and $D$ be a normal crossing divi…

The study characterizes wobbly rank-2 bundles on Riemann surfaces using spectral curves.

In this paper we consider a canonical compactification of Hitchin's moduli space of stable Higgs bundles with fixed determinant of odd degree over a Riemann surface, producing a projective variety by gluing in a divisor at infinity. We give a detailed study of the compactified space, the divisor at infinity and the mod…

Constructs geometric models for moduli spaces of Higgs bundles over Riemann sphere.

The paper studies minimal surfaces in complex hyperbolic spaces, showing moduli space connected components.

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

The paper constructs solutions for Higgs fields on a 4-punctured sphere.

The study shows how energy density of harmonic maps dominates in $n$-Fuchsian fibers, leading to unique minimal surfaces.

Proves conditions for minimal surfaces in complex hyperbolic space.

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 bundle when the generalized complex manifold is ordinary complex. Schwarzenberger's r…

Identifies images of determinant morphism for specific co-Higgs bundles.

Study finds conditions for minimum of Donaldson's functional on Higgs bundles with non-holomorphic Higgs fields.

The paper extends orthogonal decomposition results to hermitian Higgs bundles.

Generalizes Higgs bundles theory using a vector bundle twist.

Study on harmonic metrics for rank 3 Higgs bundles in Hitchin section.

Study uses Vinberg pairs for Higgs bundles, revealing their role.

In this paper, we consider the gradient flow of the Yang-Mills-Higgs functional for Higgs pairs on a Hermitian vector bundle $(E, H_{0})$ over a compact Kähler manifold $(M, ω)$. We study the asymptotic behavior of the Yang-Mills-Higgs flow for Higgs pairs at infinity, and show that the limiting Higgs sheaf is isomorph…

New Poisson structures found on Higgs bundle moduli spaces.

Survey on $2k$-Hitchin equations and Higgs bundles from geometric perspective.

We consider the gradient flow of the Yang-Mills-Higgs functional of twist Higgs pairs on a Hermitian vector bundle $(E,H_0)$ over a Riemann surface $X$. It is already known the gradient flow with initial data $(A_0,φ_0)$ converges to a critical point $(A_\infty, φ_\infty)$ of this functional. Using a modified Chern-Wei…

Classifies very stable Higgs bundles for complex groups.

Study Higgs bundles and their reductions to prove stability and cohomology properties.

Diagonal metrics solve Hermitian-Einstein equations for decomposed Higgs bundles.

In this note, by using the Yang-Mills-Higgs flow, we show that semistable Higgs bundles with vanishing the first and second Chern numbers over compact Käher manifolds must admit a filtration whose quotients are Hermitian flat Higgs bundles.

We generalize the classical Beauville-Narasimhan-Ramanan correspondence to the case of parabolic Higgs bundles with regular singularities and Higgs $V$-bundles. Using this correspondence along with Bott-Morse theoretic techniques we provide an exact component count for moduli spaces of maximal parabolic $\text{Sp}\left…

Develops Lie-theoretic perspective on Hitchin's equations for cyclic G-Higgs bundles.

Defines and classifies toric co-Higgs bundles on projective toric varieties.

We provide notions of numerical effectiveness and numerical flatness for Higgs vector bundles on compact Kähler manifolds in terms of fibre metrics. We prove several properties of bundles satisfying such conditions and in particular we show that numerically flat Higgs bundles have vanishing Chern classes, and that they…

We introduce the notion of Hermitian Higgs bundle as a natural generalization of the notion of Hermitian vector bundle and we study some vanishing theorems concerning Hermitian Higgs bundles when the base manifold is a compact complex manifold. We show that a first vanishing result, proved for these objects when the ba…

In this article, we study the Higgs vector bundles $(E,θ)$ over a compact Calabi-Yau manifolds $X$. We use Yang-Mills-Higgs flow to prove that if a semistable Higgs bundle with vanishing Chern classes over a compact connected Calabi-Yau manifold, then the Higgs field $θ$ is trivial. In particular, the vector bundle $E$…

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

Study Poisson metrics on noncompact Kähler manifolds and their Higgs bundle applications.

We prove a Hitchin-Kobayashi correspondence for extensions of Higgs bundles. The results generalize known results for extensions of holomorphic bundles. Using Simpson's methods, we construct moduli spaces of stable objects. In an appendix we construct Bott-Chern forms for Higgs bundles

Study generalizes Hermitian-Einstein equation for cyclic Higgs bundles, proving existence and inequality.

Co-Higgs bundles are Higgs bundles in the sense of Simpson, but with Higgs fields that take values in the tangent bundle instead of the cotangent bundle. Given a vector bundle on P^1, we find necessary and sufficient conditions on its Grothendieck splitting for it to admit a stable Higgs field. We characterize the rank…

A new class of Higgs bundles is introduced in a natural setting. Existence and nonexistence results for Higgs-Hermitian-Yang-Mills metrics are proved.

Fix a $C^\infty$ principal $G$--bundle $E^0_G$ on a compact connected Riemann surface $X$, where $G$ is a connected complex reductive linear algebraic group. We consider the gradient flow of the Yang--Mills--Higgs functional on the cotangent bundle of the space of all smooth connections on $E^0_G$. We prove that this f…

This paper generalizes a topological invariant to cyclic Higgs bundles.

In this paper, we study Higgs bundles on non-compact Hermitian manifolds. Under some assumptions for the underlying Hermitian manifolds which are not necessarily Kähler, we solve the Hermitian-Einstein equation on analytically stable Higgs bundles.