Arakelov inequalities and semistable families of curves uniformized by the unit ball

Leiden Repository

Arakelov inequalities and semistable families of curves uniformized by the unit ball

Type: Doctoral Thesis
Title: Arakelov inequalities and semistable families of curves uniformized by the unit ball
Author: Damjanovic, N.
Issue Date: 2018-06-14
Keywords: Cyclic coverings
Semistable families of curves
Variations of Hodge structures
Higgs bundles
Ball quotients
Teichmüller curves
Abstract: The main object of study in this thesis is an Arakelov inequalitywhich bounds the degree of an invertible subsheaf of the direct image ofthe pluricanonical relative sheaf of a semistable family of curves. A naturalproblem that arises is the characterization of those families for which the equalityis satisfied in that Arakelov inequality, i.e. the case of Arakelov equality.Few examples of such families are known. In this thesis we provide some examplesby proving that the direct image of the bicanonical relative sheaf ofa semistable family of curves uniformized by the unit ball, all whose singularfibers are totally geodesic, contains an invertible subsheaf which satisfiesArakelov equality.
Promotor: Supervisor: Koziarz V., Edixhoven S. Co-Supervisor: Jong R. de
Faculty: Science
University: Leiden
Handle: http://hdl.handle.net/1887/63084
 

Files in this item

Description Size View
application/pdf Full Text 1.805Mb View/Open
application/pdf Title Page_Contents 1.025Mb View/Open
application/pdf Chapter 01 437.4Kb View/Open
application/pdf Chapter 02 510.3Kb View/Open
application/pdf Chapter 03 456.5Kb View/Open
application/pdf Chapter 04 499.0Kb View/Open
application/pdf Bibliography_Acknowledgements_CV 297.9Kb View/Open
application/pdf Summary_in Dutch 278.5Kb View/Open
application/pdf Propositions 193.9Kb View/Open

This item appears in the following Collection(s)