Related papers: Some kernels on a Riemann surface
The free Baker-Akhiezer modules on rational varieties obtained from ${\mathbb C}P^{1}\times{\mathbb C}P^{n-1}$ by identification of two hypersurfaces are constructed. The corollary of this construction is the existence of embedding of…
In this paper continuing our work started in our earlier papers we prove the corona theorem for the algebra of bounded holomorphic functions defined on an unbranched covering of a Caratheodory hyperbolic Riemann surface of finite type.
The generators of the group of birational automorphisms of any Severi-Brauer surface non-isomorphic over an algebraically non-closed field to the projective plane are explicitly described.
We prove that the Bergman kernel function associated to a smooth measure supported on a piecewise-smooth maximally totally real submanifold K in C^n is of polynomial growth (e.g, in dimension one, K is a finite union of transverse Jordan…
If a (non-constant) polynomial has no zero, then a certain Riemannian metric is constructed on the two dimensional sphere. Several geometric arguments are then shown to contradict this fact.
An explicit canonical construction of monopole connections on non trivial U(1) bundles over Riemann surfaces of any genus is given. The class of monopole solutions depend on the conformal class of the given Riemann surface and a set of…
Motivated by the construction of Bach flat neutral signature Riemannian extensions, we study the space of parallel trace free tensors of type $(1,1)$ on an affine surface. It is shown that the existence of such a parallel tensor field is…
In this paper we continue to investigate a certain class of Hankel-like positive definite kernels using their associated orthogonal polynomials. The main result of this paper is about the structure of this kind of kernels.
In this note, we explain that Ross-Thomas' result on the weighted Bergman kernels on orbifolds can be directly deduced from our previous result. This result plays an important role in the companion paper to prove an orbifold version of…
The kernel method is an essential tool for the study of generating series of walks in the quarter plane. This method involves equating to zero a certain polynomial, the kernel polynomial, and using properties of the curve, the kernel curve,…
In this note we discuss the geometry of Riemannian surfaces having a discrete set of singular points. We assume the conformal structure extends through the singularities and the curvature is integrable. Such points are called \emph{simple…
This is an introduction to the geometry of compact Riemann surfaces, largely following the books Farkas-Kra, Fay, Mumford Tata lectures. 1) Defining Riemann surfaces with atlases of charts, and as locus of solutions of algebraic equations.…
Herein we prove that if $M$ is a compact oriented Riemann surface of genus $g$, and $M^{[n]}$ is the classifying space of $n$ distinct, unordered points on $M$, then the kernel of the map $\pi_1(M^{[n]})\to H_1(M)$ is generated by…
We describe a notion of ampleness for line bundles on orbifolds with cyclic quotient singularities that is related to embeddings in weighted projective space, and prove a global asymptotic expansion for a weighted Bergman kernel associated…
The goal of this note is to explore the Bergman projection on forms. In particular, we show that some of most basic facts used to construct the Bergman kernel on functions, such as pointwise evaluation in…
In $\mathbb R^d$, it is well-known that cumulants provide an alternative to moments that can achieve the same goals with numerous benefits such as lower variance estimators. In this paper we extend cumulants to reproducing kernel Hilbert…
In this article, we study some properties of the $n$-th order weighted reduced Bergman kernels for planar domains, $n\geq 1$. Specifically, we look at Ramadanov type theorems, localization, and boundary behaviour of the weighted reduced…
The paper introduces a new characterisation of strictly positive definiteness for kernels on the 2-sphere without assuming the kernel to be radially (isotropic) or axially symmetric. The results use the series expansion of the kernel in…
Kernel theorems, in general, provide a convenient representation of bounded linear operators. For the operator acting on a concrete function space, this means that its action on any element of the space can be expressed as a generalised…
We develop a theory of holomorphic differentials on a certain class of non-compact Riemann surfaces obtained by opening infinitely many nodes.