Related papers: Parabolic bundles and spherical metrics

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 introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their radii are described by a discrete integrable system. This is…

We study parabolic G-Higgs bundles over a compact Riemann surface with fixed punctures, when G is a real reductive Lie group, and establish a correspondence between these objects and representations of the fundamental group of the punctured…

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…

Let $E$ be a smooth bundle with fiber an $n$-dimensional real projective space $\mathbb{R}P^n$. We show that, if every fiber carries a positively curved pointwise strongly $1/4$-pinched Riemannian metric that varies continuously with…

Given a tuple of holomorphic differentials on a Riemann surface, one can define a Higgs bundle in the Hitchin section and a natural symmetric pairing of the Higgs bundle. We study whether a Higgs bundle of rank 3 in the Hitchin section has…

In this paper, we establish the Hitchin--Kobayashi correspondence for the $I_\pm$-holomorphic quiver bundle $\mathcal{E}=(E,\phi)$ over a compact generalized K\"{a}hler manifold $(X, I_+,I_-,g, b)$ such that $g$ is Gauduchon with respect to…

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…

An explicit formula for the generalized hyperbolic metric on the thrice--punctured sphere $\P \backslash \{z_1, z_2, z_3\}$ with singularities of order $\alpha_j \le 1$ at $z_j$ is obtained in all possible cases $\alpha_1+\alpha_2+\alpha_3…

In this article we completely describe the existence of canonical metrics, known as optimal symplectic connections, on isotrivial K\"ahler fibrations. In this setting an optimal symplectic connection is induced from a Hermite--Einstein…

We introduce equations for special metrics, and notions of stability for some new types of augmented holomorphic bundles. These new examples include holomorphic extensions, and in this case we prove a Hitchin-Kobayashi correspondence…

In this paper we use the relationship between conformal metrics on the sphere and horospherically convex hypersurfaces in the hyperbolic space for giving sufficient conditions on a conformal metric to be radial under some constrain on the…

Let $X$ be a compact Riemann surface and $\mathbb{P}^1$ be the complex projective line. In this paper, we introduce an equation which we call the doubly-coupled vortex equation on $X$. We show that the existence of a solution of the…

We extract a new class of paracontact paracomplex Riemannian manifolds arising from certain cone construction, call it para-Sasaki-like Riemannian manifold and give explicit examples. We define a hyperbolic extension of a paraholomorphic…

In this article we address a number of features of the moduli space of spherical metrics on connected, compact, orientable surfaces with conical singularities of assigned angles, such as its non-emptiness and connectedness. We also consider…

This article describes an entirely algebraic construction for developing conformal geometries, which provide models for, among others, the Euclidean, spherical and hyperbolic geometries. On one hand, their relationship is usually shown…

In this paper, we present an algebro-geometric construction of the Hitchin connection in the parabolic setting for a fixed determinant line bundle. Our strategy is based on Hecke modifications, where we provide a decomposition formula for…

In this paper, we introduce the notions of parabolic representation pair variety and relative representation variety of a given parabolic type. We investigate the local behavior of these varieties. The Zariski tangent space and the tangent…

We present a geometric mechanism for the emergence of spherical $3$-manifolds from the superspace of Riemannian metrics associated with flat ${\rm{SU}}(2)$-bundles over closed orientable hyperbolic surfaces. Our main result shows that any…

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…