Related papers: Constructing stable Hilbert bundles via Diophantin…

We give a new construction of strict deformation quantization of symplectic manifolds equipped with a proper Lagrangian fiber bundle structure, whose representation spaces are the quantum Hilbert spaces obtained by geometric quantization.…

In this paper, we study the regular quantizations of K\"{a}hler manifolds by using the first two coefficients of Bergman function expansions. Firstly, we obtain sufficient and necessary conditions for certain Hermitian holomorphic vector…

We study a tower of normal coverings over a compact K\"ahler manifold with holomorphic line bundles. When the line bundle is sufficiently positive, we obtain an effective estimate, which implies the Bergman stability. As a consequence, we…

A refined notion of curvature for a linear system of Hermitian vector spaces, in the sense of Grothendieck, leads to the unitary classification of a large class of analytic Hilbert modules. Specifically, we study Hilbert sub-modules, for…

Let $X$ be a compact Riemann surface. Let $(E,\theta)$ be a stable Higgs bundle of degree $0$ on $X$. Let $h_{\det(E)}$ denote a flat metric of the determinant bundle $\det(E)$. For any $t>0$, there exists a unique harmonic metric $h_t$ of…

We prove that the existence of a $Z$-positive and $Z$-critical Hermitian metric on a rank 2 holomorphic vector bundle over a compact K\"ahler surface implies that the bundle is $Z$-stable. As particular cases, we obtain stability results…

We construct smooth bundles with base and fiber products of two spheres whose total spaces have non-vanishing $\hat{A}$-genus. We then use these bundles to locate non-trivial rational homotopy groups of spaces of Riemannian metrics with…

This paper is concerned with a relative uniform Yau--Tian--Donaldson correspondence, in terms of test configurations, for the projectivization \( \mathbb{P}(E) \) of a holomorphic vector bundle \( E \) over a smooth curve. For any K\"ahler…

The aim of this paper is twofold. First we prove a theorem of extension of sections of a coherent subquotient of a hermitian vector bundle on a complex analytic space with control of the norms, without any of the smoothness assumptions that…

An ansatz of Calabi allows construction of Kahler metrics in an Hermitian disk bundle over a Kahler manifold. We attempt to give a definitive treatment of this ansatz, with the following results: We give curvature conditions on the disk…

A flat complex vector bundle (E,D) on a compact Riemannian manifold (X,g) is stable (resp. polystable) in the sense of Corlette [C] if it has no D-invariant subbundle (resp. if it is the D-invariant direct sum of stable subbundles). It has…

We consider a notion of balanced metrics for triples (X,L,E) which depend on a parameter \alpha, where X is smooth complex manifold with an ample line bundle L and E is a holomorphic vector bundle over X. For generic choice of \alpha, we…

In this paper, we consider the existence of approximate Hermitian-Einstein structure and the semi-stability on Higgs bundles over compact Gauduchon manifolds. By using the continuity method, we show that they are equivalent.

We study the linear stability of Einstein metrics of Riemannian submersion type. First, we derive a general instability condition for such Einstein metrics and provide some applications. Then we study instability arising from Riemannian…

Given a flat vector bundle over a compact Riemannian manifold, Corlette and Donaldson proved that it admits harmonic metrics if and only if it is semi-simple. In this paper, we extend this equivalence to arbitrary vector bundles without any…

The aim of this paper is to study Seifert bundle structures on simply connected 5--manifolds. We classify all such 5--manifolds which admit a Seifert bundle structure, and in a few cases all Seifert bundle structures are also classified.…

Unstable holomorphic bundles can be described algebraically by Harder-Narasimhan filtrations. In this note we show how such filtrations correspond to the existence of special metrics defined by Hermitian-Einstein inequalities.

We give a differential geometric construction of a connection in the bundle of quantum Hilbert spaces arising from half-form corrected geometric quantization of a prequantizable, symplectic manifold, endowed with a rigid, family of K\"ahler…

The Hilbert scheme of n points in the projective plane parameterizes degree n zero-dimensional subschemes of the projective plane. We examine the dual cones of effective divisors and moving curves on the Hilbert scheme. By studying…

We study orthogonal polynomial systems arising from general pre-Hilbert inner products on polynomial spaces, beyond the classical framework of measures. To each such inner product we associate a canonical Laplacian defined from an abstract…