Citation
van Garrel, Michel (2013) Relative Mirror Symmetry and Ramifications of a Formula for Gromov-Witten Invariants. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/9EQP-PD83. https://resolver.caltech.edu/CaltechTHESIS:05312013-164406051
Abstract
For a toric Del Pezzo surface S, a new instance of mirror symmetry, said relative, is introduced and developed. On the A-model, this relative mirror symmetry conjecture concerns genus 0 relative Gromov-Witten of maximal tangency of S. These correspond, on the B-model, to relative periods of the mirror to S. Furthermore, for S not necessarily toric, two conjectures for BPS state counts are related. It is proven that the integrality of BPS state counts of the total space of the canonical bundle on S implies the integrality for the relative BPS state counts of S. Finally, a prediction of homological mirror symmetry for the open complement is explored. The B-model prediction is calculated in all cases and matches the known A-model computation for the projective plane.
Item Type: | Thesis (Dissertation (Ph.D.)) |
---|---|
Subject Keywords: | Relative Mirror Symmetry, BPS state counts, Gromov-Witten invariants, Open Complement, Homological Mirror Symmetry, Algebraic Geometry, Symplectic Geometry |
Degree Grantor: | California Institute of Technology |
Division: | Physics, Mathematics and Astronomy |
Major Option: | Mathematics |
Awards: | Apostol Award for Excellence in Teaching in Mathematics, 2011. |
Thesis Availability: | Public (worldwide access) |
Research Advisor(s): |
|
Thesis Committee: |
|
Defense Date: | 21 May 2013 |
Record Number: | CaltechTHESIS:05312013-164406051 |
Persistent URL: | https://resolver.caltech.edu/CaltechTHESIS:05312013-164406051 |
DOI: | 10.7907/9EQP-PD83 |
Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
ID Code: | 7807 |
Collection: | CaltechTHESIS |
Deposited By: | Michel Francois Van Garrel |
Deposited On: | 03 Jun 2013 22:24 |
Last Modified: | 04 Oct 2019 00:01 |
Thesis Files
|
PDF
- Final Version
See Usage Policy. 416kB |
Repository Staff Only: item control page