Related papers: Bergman kernels on degenerations

Let $A$ be abelian variety over the function field $K$ of a compact Riemann surface $B$. Fix a model $f \colon \mathcal{A} \to B$ of $A/K$ and a certain effective horizontal divisor $\DD \subset \mathcal{A}$. We give a sufficient condition…

We reduce the problem of the projective normality of polarized abelian varieties to check the rank of very explicit matrices. This allow us to prove some results on normal generation of primitive line bundles on abelian threefolds and…

We prove a continuity result for the fibers of the Berkovich analytification of a complex algebraic variety with respect to the the maximum of the Archimedean norm and the trivial norm. As a consequence, we obtain generalizations of a…

A theorem of Wiegerinck asserts that the Bergman space of an open subset of the complex numbers is either infinite-dimensional or trivial. Recently, this has been generalized to holomorphic vector bundles over the projective line by the…

Every smooth fiber bundle admits a complete (Ehresmann) connection. This result appears in several references, with a proof on which we have found a gap, that does not seem possible to remedy. In this note we provide a definite proof for…

Let S be a smooth affine algebraic curve, and let S' be the Riemann surface obtained by removing a point from S. We provide evidence for the congruence subgroup property of the mapping class group Mod(S') by showing that its congruence…

In this paper we continue the study of Bergman theory for the class of slice regular functions. In the slice regular setting there are two possibilities to introduce the Bergman spaces, that are called of the first and of the second kind.…

We calculate curvature tensors of metrics on the total spaces of holomorphic fibrations. Our main tool is a theory of Chern connections and curvature forms for possibly degenerate Hermitian forms on holomorphic vector bundles. We prove a…

We prove convergence to equilibrium for a class of coagulation-fragmentation equations that do not satisfy a detailed balance condition. More precisely, we consider perturbations of constant rate kernels. Our result provides in particular…

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…

According to Laumon, an affine Springer fiber is homeomorphic to the universal abelian covering of the compactified Jacobian of a spectral curve. We construct equivariant deformations $f_{n}:\overline{\mathcal{P}}_{n}\to \mathcal{B}_{n}$ of…

In this article, we consider Bergman kernels related to modules at boundary points on Stein manifolds, and obtain a log-subharmonicity property of the Bergman kernels. As applications, we obtain a lower estimate of weighted $L^2$ integrals…

We show how the formalism of Frobenius descent for torsors enables to study torsors under Frobenius kernels in terms of non-commutative, Lie-valued differential forms. We pay particular attention to affine line bundles trivialized by the…

Given a compact Riemann surface $Y$ and a positive integer $m$, Narasimhan and Simha defined a measure on $Y$ associated to the $m$-th tensor power of the canonical line bundle. We study the limit of this measure on holomorphic families of…

In the present paper, we generalize the notion of the $p$-Bergman kernel and the $\xi$-Bergman kernel to the $p$-Bergman kernel with respect to a functional $\xi$, and establish some properties of the $p$-Bergman kernel with respect to…

This is a sequel of our paper [arXiv:1809.08425] on the Quot-scheme limit and variational properties of Donaldson's functional, which established its coercivity for slope stable holomorphic vector bundles over smooth projective varieties.…

When analyzing modern machine learning algorithms, we may need to handle kernel density estimation (KDE) with intricate kernels that are not designed by the user and might even be irregular and asymmetric. To handle this emerging challenge,…

Consider a complex line bundle over a compact complex manifold equipped with an infinitely differentiable metric with strictly positive curvature form. Assign to positive tensor powers of this bundle the associated product metrics and…

We prove constancy of Newton polygons of all convergent $F$-isocrystals on Abelian varieties over finite fields. Applying the constancy, we prove the isotriviality of projective smooth families of curves over Abelian varieties. We also…

This article concerns properties of mixed $\ell$-adic complexes on varieties over finite fields, related to the action of the Frobenius automorphism. We establish a fiberwise criterion for the semisimplicity and Frobenius semisimplicity of…