Jost, Jan Niklas
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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 |
