Jost, Jan Niklas
Preview |
PDF, English
Download (920kB) | Terms of use |
Citation of documents: Please do not cite the URL that is displayed in your browser location input, instead use the DOI, URN or the persistent URL below, as we can guarantee their long-time accessibility.
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.
Document type: | Dissertation |
---|---|
Supervisor: | Reichelt, Dr. Thomas |
Place of Publication: | Heidelberg |
Date of thesis defense: | 26 January 2021 |
Date Deposited: | 18 Feb 2021 10:00 |
Date: | 2021 |
Faculties / Institutes: | The Faculty of Mathematics and Computer Science > Institut für Mathematik |
DDC-classification: | 500 Natural sciences and mathematics 510 Mathematics |