Related papers: The Szeg\"O kernel on an orbifold circle bundle

Given a complete K\"ahler manifold $(X,\,\omega)$ with finite second Betti number, a smooth complex hypersurface $Y\subset X$ and a smooth real $d$-closed $(1,\,1)$-form $\alpha$ on $X$ with arbitrary, possibly non-rational, De Rham…

We study the relationship between the geometry and the Laplace spectrum of a Riemannian orbifold O via its heat kernel; as in the manifold case, the time-zero asymptotic expansion of the heat kernel furnishes geometric information about O.…

Let $(G,\kappa)$ be a compact connected Lie group endowed with a biinvariant Riemannian metric, and let $\tilde{G}$ be the complexification of $G$. We apply Grauert tube techniques to the near-diagonal scaling asymptotics of certain…

For a class of $O(n+1,R)$ invariant measures on the Kepler manifold possessing finite moments of all orders, we describe the reproducing kernels of the associated Bergman spaces, discuss the corresponding asymptotic expansions of…

Let $( X ,d ,p ) $ be the pointed Gromov-Hausdorff limit of a sequence of pointed complete polarized K\"ahler manifolds $( M_l ,\omega_l ,\mathcal{L}_l ,h_l ,p_l ) $ with $Ric ( h_l ) =2\pi \omega_l $, $Ric ( \omega_l ) \geq -\Lambda…

Let S be a compact connected oriented orbifold surface We show that using Bers simultaneous uniformization, the moduli space of projective structure on S can be mapped biholomorphically onto the total space of the holomorphic cotangent…

We study function theory and K\"ahler geometry on total spaces of vector bundles on an elliptic curve. For rank two vector bundles of degree zero, we show that any two total spaces are biholomorphic if and only if the corresponding vector…

Hyperholomorphic bundle is a bundle with connection defined over a hyperkaehler manifold such that this connection is holomorphic with respect to all complex structures induced by a hyperkaehler structure. A hyperholomorphic connection is…

In this paper we obtain an explicit formula of Cauchy--Szeg\"{o} kernel for quaternionic Siegel upper half space, and then based on this, we prove that the Cauchy--Szeg\"{o} projection on quaternionic Heisenberg group is a…

In this paper, we develop a new scaling method to study spectral and Bergman kernels for the k-th tensor power of a line bundle over a complex manifold under local spectral gap condition. In particular, we establish a simple proof of the…

We generalize the results of Montgomery for the Bochner Laplacian on high tensor powers of a line bundle. When specialized to Riemann surfaces, this leads to the Bergman kernel expansion and geometric quantization results for semi-positive…

We study manifolds arising as spaces of sections of complex manifolds fibering over the projective line with normal bundle of each section isomorphic to several copies of O(k). Such manifolds provide a natural setting for certain integrable…

Graded skew-commutative rings occur often in practice. Here are two examples: 1) The cohomology ring of a compact three-dimensional manifold. 2) The cohomology ring of the complement of a hyperplane arrangement (the Orlik-Solomon algebra).…

We investigate the Cauchy--Szeg\H{o} projection for quaternionic Siegel upper half space to obtain the pointwise (higher order) regularity estimates for Cauchy--Szeg\H{o} kernel and prove that the Cauchy--Szeg\H{o} kernel is non-zero…

A Szeg\"o-type theorem for Toeplitz operators was proved by Boutet de Monvel and Guillemin for general Toeplitz structures. We give a local version of this result in the setting of positive line bundles on compact symplectic manifolds.

Graded skew-commutative rings occur often in practice. Here are two examples: 1) The cohomology ring of a compact three-dimensional manifold. 2) The cohomology ring of the complement of a hyperplane arrangement (the Orlik-Solomon algebra).…

Let $M=P(E)$ be the complex manifold underlying the total space of the projectivization of a holomorphic vector bundle $E \to \Sigma$ over a compact complex curve $\Sigma$ of genus $\ge 2$. Building on ideas of Fujiki, we prove that $M$…

Let $M$ be a Kaehler manifold, and consider the total space $T^*M$ of the cotangent bundle to $M$. We show that in the formal neighborhood of the zero section $M \subset T^*M$ the space $T^*M$ admits a canonical hyperkaehler structure,…

On asymptotically complex hyperbolic (ACH) Einstein manifolds, we consider a certain variational problem for almost complex structures compatible with the metric, for which the linearized Euler-Lagrange equation at K\"ahler-Einstein…

Using the machinery of unitary spherical harmonics due to Koornwinder, Folland and other authors, we~obtain expansions for the Szeg\"o and the weighted Bergman kernels of $M$-harmonic functions, i.e.~functions annihilated by the invariant…