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Relative Gromov-Witten Invariants - A Computation

Dolfen, Clara

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 ๐”ฝโ‚ = โ„™(๐’ช_โ„™ยน โŠ• ๐’ช_โ„™ยน (1)) relative to the divisor ๐ท = ๐ต + ๐น, where ๐ต is the base and ๐น the fiber of the projective bundle. We will provide an explicit description of the connected components of the fixed locus of the moduli space ๐‘€ฬ…โ‚€,๐‘› (๐”ฝโ‚ ; ๐ท|๐›ฝ ; ๐œ‡) using decorated colored graphs and further determine the weight decomposition of their virtual normal bundles. This thesis contains explicit computations for ๐œ‡ = (3) and ๐›ฝ = 3๐น + ๐ต), and additionally ๐œ‡ = (4) and ๐›ฝ โˆˆ {4๐น + ๐ต, 4๐น + 2๐ต}. The same methodology however can be applied to any other ramification pattern ๐œ‡ and curve class ๐›ฝ.


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More About This Work

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