eprintid: 29359
rev_number: 17
eprint_status: archive
userid: 5700
dir: disk0/00/02/93/59
datestamp: 2021-02-18 10:00:36
lastmod: 2021-02-26 06:29:25
status_changed: 2021-02-18 10:00:36
type: doctoralThesis
metadata_visibility: show
creators_name: Jost, Jan Niklas
title: Mirror Symmetry for Del Pezzo Surfaces
subjects: ddc-500
subjects: ddc-510
divisions: i-110400
adv_faculty: af-11
abstract: We describe mirror symmetry as an equivalence of D-modules. On the A-side we give an introduction to Gromov-Witten invariants, quantum cohomology and the Dubrovin connection. In particular we compute the small quantum cohomology for Del Pezzo surfaces in general and the Dubrovin connection for X_4 explicitly. On the B-side a mirror D-module is constructed as some Fourier-Laplace transformed Gauß-Manin system. We consider its Brieskorn lattice and explicitly compute it for the toric variety X^o_4. Furthermore we derive a solution to Birkhoff’s problem by determining concretely a good basis in the sense of M. Saito. Consequently we prove a mirror theorem for X_4.
date: 2021
id_scheme: DOI
id_number: 10.11588/heidok.00029359
ppn_swb: 1749466880
own_urn: urn:nbn:de:bsz:16-heidok-293592
date_accepted: 2021-01-26
advisor: HASH(0x55fc36c9f408)
language: eng
bibsort: JOSTJANNIKMIRRORSYMM2021
full_text_status: public
place_of_pub: Heidelberg
citation:   Jost, Jan Niklas  (2021) Mirror Symmetry for Del Pezzo Surfaces.  [Dissertation]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/29359/1/Dissertation.pdf