2021 Theses Doctoral

# Relative Gromov-Witten Invariants - A Computation

We will compute relative Gromov--Witten invariants of maximal contact order by applying the virtual localization formula to the moduli space of relative stable maps. In particular, we will enumerate genus 0 stable maps to the Hirzebruch surface ๐ฝโ = โ(๐ช_โยน โ ๐ช_โยน (1)) relative to the divisor ๐ท = ๐ต + ๐น, where ๐ต is the base and ๐น the fiber of the projective bundle. We will provide an explicit description of the connected components of the fixed locus of the moduli space ๐ฬ โ,๐ (๐ฝโ ; ๐ท|๐ฝ ; ๐) using decorated colored graphs and further determine the weight decomposition of their virtual normal bundles. This thesis contains explicit computations for ๐ = (3) and ๐ฝ = 3๐น + ๐ต), and additionally ๐ = (4) and ๐ฝ โ {4๐น + ๐ต, 4๐น + 2๐ต}. The same methodology however can be applied to any other ramification pattern ๐ and curve class ๐ฝ.

## Files

- Dolfen_columbia_0054D_16443.pdf application/pdf 6.16 MB Download File

## More About This Work

- Academic Units
- Mathematics
- Thesis Advisors
- Liu, Chiu-Chu
- Degree
- Ph.D., Columbia University
- Published Here
- April 21, 2021