Work

Bergman spaces on algebraic curves

Year: 2026

Type: article

Abstract: 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 third author and later to vector bundles over any compact Riemann surface by Gallagher, Gupta and Vivas. In the present paper we extend the above results to the case of certain singular metrics associated to divisors on a Riemann surface. As corollaries we obtain versions of Wiegerinck’s theorem for both projective and affine algebraic curves.

Source: Mathematische Zeitschrift

DOI: 10.1007/s00209-026-04027-2

Authors: László Koltai, Alexander A. Kubasch, Róbert Szőke

Institutions: Eötvös Loránd University, HUN-REN Alfréd Rényi Institute of Mathematics

Language: English

Topic: Holomorphic and Operator Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

OpenAlex ID: W7160704885