Families of Line Bundles over Riemann Surfaces, their Sections, and their Degenerations -- A Constructive Approach using Automorphic Forms

摘要

In this paper we study the deformation problem of pairs consisting of aRiemann surface and a holomorphic line bundle over that surface, and alsosections thereof. We emphasize a constructive approach throughout and work anduse covering space techniques. In particular, we also describe the limits ofsuch degenerations as the boundary of Teichm\"uller space is approached, andreview the construction of augmented Teichm\"uller space in great detail.