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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
72/2009

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

Guy Buss

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 Teichm\"uller space is approached, and review the construction of augmented Teichm\"uller space in great detail.

Received:
Dec 9, 2009
Published:
Dec 10, 2009
MSC Codes:
30F30, 30F35, 30F60, 32L05, 32N10
Keywords:
Automorphic Forms, Teichmueller Space, Degenerations

Related publications

Preprint
2009 Repository Open Access
Guy Buss

Families of line bundles over Riemann surfaces, their sections, and their degenerations : a constructive approach using automorphic forms