Date of Award
Spring 2024
Project Type
Dissertation
Program or Major
Physics
Degree Name
Doctor of Philosophy
First Advisor
Per Berglund
Second Advisor
Maria Basterra
Third Advisor
David Mattingly
Abstract
Correlation functions in the topological A-model can be computed with open Gromov-Witten invariants whereas the mirror topological B-model admits a simpler description in terms of period integrals. We first review preliminary material in Chapter 1. Then in Chapter 2 we use tropical geometry to construct the Duistermaat-Heckman measure for non-Fano toric varieties. This allows one to compute the asymptotic terms of period integrals. In Chapter 3 we solve the generalized Picard-Fuchs system for the Hirzebruch surfaces, and hence compute periods to all orders of the mirror complex structure moduli. Near the large complex structure limit point, we use toric degenerations, scattering diagrams, and Landau-Ginzburg models from the Gross-Siebert mirror symmetry program to compute open Gromov-Witten invariants. The results of Chapter 3 extend the result of Gräfnitz-Ruddat-Zaslow to non-Fano toric varieties. Namely, the proper Landau-Ginzburg superpotential is the open mirror map even in the non-Fano setting. We explicitly compute invariants for the Hirzebruch surfaces and observe novel features such as internal scattering and negative kinks in the scattering diagram.
Recommended Citation
Lathwood, Michael John Samuel, "Aspects of Mirror Symmetry for Non-Fano Toric Varieties" (2024). Doctoral Dissertations. 2835.
https://scholars.unh.edu/dissertation/2835