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Mirror Symmetry for Del Pezzo Surfaces

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.

Item 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 > Department of Mathematics
Subjects: 500 Natural sciences and mathematics
510 Mathematics
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