标题： 代数曲线上的伯格曼空间 显示英文标题

标题： Bergman spaces on algebraic curves

摘要： Wiegerinck的一个定理断言，复数开子集上的Bergman空间要么是无限维的，要么是平凡的。最近，该定理由第三作者推广到射影直线上的全纯向量丛，并且后来由Gallagher、Gupta和Vivas将其推广到任意紧Riemann曲面上的向量丛。在本文中，我们将上述结果扩展到与Riemann曲面上除子相关的某些奇异性度量的情形。作为推论，我们得到了Wiegerinck定理的版本，适用于射影代数曲线和仿射代数曲线。 显示英文摘要

摘要： 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.