title: Tannakian Categories of Perverse Sheaves on Abelian Varieties
creator: Krämer, Thomas
subject: 510
subject: 510 Mathematics
description: We study Tannakian categories attached to perverse sheaves on abelian varieties with respect to the convolution product. The construction of these categories is closely intertwined with a cohomological vanishing theorem which is an analog of Artin's affine vanishing theorem and contains the generic vanishing theorems of Green and Lazarsfeld as a special case. To illustrate the geometric relevance of the developed notions, we determine the Tannaka group of the theta divisor on a general principally polarized complex abelian variety of arbitrary dimension and explain its relationship with the Schottky problem in genus 4. Here the convolution square of the theta divisor describes a family of surfaces of general type, and a detailed study of this family leads to a variation of Hodge structures with monodromy group W(E6) which has a natural interpretation in terms of the Prym map. In the final chapter we take a closer look at convolutions of curves inside Jacobian varieties and provide a recursive formula for the generic rank of Brill-Noether sheaves.  
date: 2013-06
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/15066/1/DissSubmission.pdf
identifier: DOI:10.11588/heidok.00015066
identifier: urn:nbn:de:bsz:16-heidok-150661
identifier:   Krämer, Thomas  (2013) Tannakian Categories of Perverse Sheaves on Abelian Varieties.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/15066/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng