Related papers: Approximate Hermitian-Yang-Mills structures on sem…

We introduce the notion of $T$-stability for torsion-free Higgs sheaves as a natural generalization of the notion of $T$-stability for torsion-free coherent sheaves over compact complex manifolds. We prove similar properties to the…

The self-duality equations on a Riemann surface arise as dimensional reduction of self-dual Yang-Mills equations. Hitchin had showed that the moduli space ${\mathcal M}$ of solutions of the self-duality equations on a compact Riemann…

We consider Higgs bundles satisfying a notion of numerical flatness (H-nflatness) that was previously introduced, and show that they have Jordan-H\"older filtrations whose quotients are stable, locally free and H-nflat. This is applied to…

By considering a (partial) topological twisting of supersymmetric Yang-Mills compactified on a 2d space with `t Hooft magnetic flux turned on we obtain a supersymmetric $\sigma$-model in 2 dimensions. For N=2 SYM this maps Donaldson…

In [7-9] and [10] the conjecture is presented that almost-commutative geometries, with respect to sensible physical constraints, allow only the standard model of particle physics and electro-strong models as Yang-Mills-Higgs theories. In…

In this paper, we define a family of functionals generalizing the Yang-Mills-Higgs functional on a closed Riemannian manifold. Then we prove the short time existence of the corresponding gradient flow by a gauge fixing technique. The lack…

We establish that Hitchin's connection exist for any rigid holomorphic family of Kahler structures on any compact pre-quantizable symplectic manifold which satisfies certain simple topological constraints. Using Toeplitz operators we prove…

Let $X$ be a compact Hermitian surface, and $g$ be any fixed Gauduchon metric on $X$. Let $E$ be an Hermitian holomorphic vector bundle over $X$. On the bundle $E$, Donaldson's heat flow is gauge equivalent to a flow of holomorphic…

We provide an algebraic framework for quantization of Hermitian metrics that are solutions of the Hitchin equation for Higgs bundles over a projective manifold. Using Geometric Invariant Theory, we introduce a notion of balanced metrics in…

We study the hypersymplectic geometry of the moduli space of solutions to Hitchin's harmonic map equations on a $G$-bundle. This is the split-signature analogue of Hitchin's Higgs bundle moduli space. Due to the lack of definiteness, this…

A-manifolds and A-bundles are manifolds and vector bundles modelled on a projective finitely generated module over a topological algebra A. In this paper we investigate the conditions under which an A-bundle is provided with an A-valued…

Given a generic ray of Higgs bundles $(\overline{\partial}_E, t\varphi)$, we describe the corresponding family of hermitian metrics $h_t$ solving Hitchin's equations via gluing methods. In the process, we construct a family of approximate…

We consider a gauge-invariant Ginzburg-Landau functional (also known as Abelian Yang-Mills-Higgs model) on Hermitian line bundles over closed Riemannian manifolds of dimension $n \geq 3$. Assuming a logarithmic energy bound in the coupling…

We study Miyaoka-type semistability criteria for principal Higgs G-bundles E on complex projective manifolds of any dimension. We prove that E has the property of being semistable after pullback to any projective curve if and only if…

In this paper, we analyze the asymptotic behaviour of the Hermitian-Yang-Mills flow over a compact non-K\"ahler manifold $(X,g)$ with the Hermitian metric $g$ satisfying the Gauduchon and Astheno-K\"ahler condition.

We construct a relative compactification of Dolbeault moduli spaces of Higgs bundles for reductive algebraic groups on families of projective manifolds that is compatible with the Hitchin morphism.

Let $\Sigma$ be a closed surface, $G$ a compact Lie group, not necessarily connected, with Lie algebra $g$, endowed with an adjoint action invariant scalar product, let $\xi \colon P \to \Sigma$ be a principal $G$-bundle, and pick a…

Let $(M,g)$ be a closed Riemannian $4$-manifold and let $E$ be a vector bundle over $M$ with structure group $G$, where $G$ is a compact Lie group. In this paper, we consider a new higher order Yang--Mills--Higgs functional, in which the…

We study Hamiltonian systems near a compact symplectic Morse-Bott minimum. Our first result shows that if the flow is Zoll (that is, it induces a free circle action) along a sequence of energy levels converging to the minimum, then the…

The main goal of this paper is to generalize a part of the relationship between mean curvature and Harder-Narasimhan filtrations of holomorphic vector bundles to arbitrary polarized fibrations. More precisely, for a polarized family of…