Vorschau

PDF, Englisch Download (920kB) | Nutzungsbedingungen

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.