%0 Generic
%A Jost, Jan Niklas
%C Heidelberg
%D 2021
%F heidok:29359
%R 10.11588/heidok.00029359
%T Mirror Symmetry for Del Pezzo Surfaces
%U https://archiv.ub.uni-heidelberg.de/volltextserver/29359/
%X 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.