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

Guy Buss

Contact the author: Please use for correspondence this email.
Submission date: 09. Dec. 2009
Pages: 61
Bibtex
MSC-Numbers: 30F30, 30F35, 30F60, 32L05, 32N10
Keywords and phrases: Automorphic Forms, Teichmueller Space, Degenerations
Download full preprint: PDF (550 kB)

Abstract:
In this paper we study the deformation problem of pairs consisting of a Riemann surface and a holomorphic line bundle over that surface, and also sections thereof. We emphasize a constructive approach throughout and use covering space techniques. In particular, we also describe the limits of such degenerations as the boundary of Teichmüller space is approached, and review the construction of augmented Teichmüller space in great detail.