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Relative Mirror Symmetry and Ramifications of a Formula for Gromov-Witten Invariants


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.


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):
  • Graber, Thomas B.
Thesis Committee:
  • Graber, Thomas B. (chair)
  • Ramakrishnan, Dinakar
  • Flach, Matthias
  • Tian, Zhiyu
Defense Date:21 May 2013
Record Number:CaltechTHESIS:05312013-164406051
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7807
Deposited By: Michel Francois Van Garrel
Deposited On:03 Jun 2013 22:24
Last Modified:04 Oct 2019 00:01

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