Related papers: M\'etriques hyperk\"ahl\'eriennes pli\'ees

We study the asymptotic hyperk\"ahler geometry of the $\mathrm{SL}_2(\mathbb{C})$-Hitchin moduli space over the singular fibers of the Hitchin fibration. We extend the previously known exponential convergence results for solutions to the…

The moduli space of stable Higgs bundles of degree $0$ is equipped with the hyperk\"ahler metric, called the Hitchin metric. On the locus where the spectral curves are smooth, there is the hyperk\"ahler metric called the semi-flat metric,…

Let $X$ be an arbitrary non-compact hyperbolic Riemann surface, that is, not $\mathbb C$ or $\mathbb C^*$. Given a tuple of holomorphic differentials $\boldsymbol q=(q_2,\cdots,q_n)$ on $X$, one can define a Higgs bundle…

We consider Hitchin's hyperk\"ahler metric $g$ on the moduli space $\mathcal{M}$ of degree zero $\mathrm{SL}(2)$-Higgs bundles over a compact Riemann surface. It has been conjectured that, when one goes to infinity along a generic ray in…

Let $X$ be a Riemann surface. Hitchin constructed the $G$-Higgs bundles in the Hitchin section for a split real form $G$ of a complex simple Lie group,using the canonical line bundle $K$ and some holomorphic differentials $\boldsymbol{q}$.…

We investigate the Hitchin hyperk\"ahler metric on the moduli space of strongly parabolic $\mathfrak{sl}(2,\C)$-Higgs bundles on the $n$-punctured Riemann sphere and its degeneration obtained by scaling the parabolic weights $t\alpha$ as…

We study metric aspects of the universal moduli space of solutions to Hitchin's equations as the complex structure $J$ varies over the Teichm\"uller space $\mathcal{T}$ of a closed surface $\Sigma$. Our approach is gauge theoretical and…

Here we survey questions and results on the Hodge theory of hyperkaehler quotients, motivated by certain S-duality considerations in string theory. The problems include L^2 harmonic forms, Betti numbers and mixed Hodge structures on the…

Freed (arXiv:hep-th/9712042) formulated special K\"ahler structures; in particular, the regular locus of the $\mathrm{SL}_2(\mathbb{C})$ Hitchin base $\mathcal{B}$ carries such a structure, while the associated metric $\omega_{\mathrm{SK}}$…

In this paper, we study the existence of Poisson metrics on flat vector bundles over noncompact Riemannian manifolds and discuss related consequence, specially on the applications in Higgs bundles, towards generalizing…

We describe the Special K\"ahler structure on the base of the so-called Hitchin system in terms of the geometry of the space of spectral curves. It yields a simple formula for the K\"ahler potential. This extends to the case of a singular…

We construct explicit examples of quaternion-K\"ahler and hypercomplex structures on bundles over hyperK\"ahler manifolds. We study the infinitesimal symmetries of these examples and the associated Galicki-Lawson quaternion-K\"ahler moment…

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…

The aim of this paper is to show the existence and give an explicit description of a pseudo-Riemannian metric and a symplectic form on the $\mathrm{S}\mathrm{L}(3,\mathbb{R})$-Hitchin component, both compatible with Labourie and Loftin's…

We study horizontal deformations of a Higgs bundle whose spectral curve is smooth. It allows us to define a natural integrable connection of the Hitchin fibration on the locus where the spectral curves are smooth. Then, in the non-zero…

A twisted Higgs bundle on a K\"ahler manifold $X$ is a pair $(E,\phi)$ consisting of a holomorphic vector bundle $E$ and a holomorphic bundle morphism $\phi\colon M\otimes E \to E$ for some holomorphic vector bundle $M$. Such objects were…

We construct a hyperk\"ahler metric on twisted cotangent bundles of the complex projective space $\mathbb{CP}^n$ explicitly in terms of local coordinates. Note that the twisted cotangent bundles of $\mathbb{CP}^n$ are holomorphically…

We study the asymptotic behavior of Hitchin's hyperk\"ahler metric on the moduli space of rank two irregular Higgs bundles over $\mathbb{C}P^1$. Along a generic curve, we prove that the Hitchin metric is asymptotic to the semiflat metric at…

We study the $2k$-Hitchin equations introduced by Ward \cite{Ward 2} from the geometric viewpoint of Higgs bundles. After an introduction on Higgs bundles and $2k$-Hitchin's equations, we review some elementary facts on complex geometry and…

Using Hitchin's parameterization of the Hitchin-Teichm\"uller component of the $SL(n,\mathbb{R})$ representation variety, we study the asymptotics of certain families of representations. In fact, for certain Higgs bundles in the…