title: Mirror Symmetry for Del Pezzo Surfaces
creator: Jost, Jan Niklas
subject: ddc-500
subject: 500 Natural sciences and mathematics
subject: ddc-510
subject: 510 Mathematics
description: 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
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/29359/1/Dissertation.pdf
identifier: DOI:10.11588/heidok.00029359
identifier: urn:nbn:de:bsz:16-heidok-293592
identifier:   Jost, Jan Niklas  (2021) Mirror Symmetry for Del Pezzo Surfaces.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/29359/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng