eprintid: 15066
rev_number: 11
eprint_status: archive
userid: 634
dir: disk0/00/01/50/66
datestamp: 2013-06-26 08:55:35
lastmod: 2013-07-02 09:58:12
status_changed: 2013-06-26 08:55:35
type: doctoralThesis
metadata_visibility: show
creators_name: Krämer, Thomas
title: Tannakian Categories of Perverse Sheaves on Abelian Varieties
subjects: 510
divisions: 110400
adv_faculty: af-11
keywords: Tannakian Categories, Perverse Sheaves, Abelian Varieties, Convolution, Vanishing theorems, Theta divisor
cterms_swd: Algebraische Geometrie
abstract: 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
id_scheme: DOI
id_number: 10.11588/heidok.00015066
ppn_swb: 1652474544
own_urn: urn:nbn:de:bsz:16-heidok-150661
date_accepted: 2013-06-13
advisor: HASH(0x5561208dc788)
language: eng
bibsort: KRAMERTHOMTANNAKIANC201306
full_text_status: public
citation:   Krämer, Thomas  (2013) Tannakian Categories of Perverse Sheaves on Abelian Varieties.  [Dissertation]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/15066/1/DissSubmission.pdf