Calabi-Yau manifolds in weighted projective space

Bachelor thesis
Research group: 
String Cosmology
Author: 
Sjoerd Bielleman
Supervisor: 
Abstract: 

Candelas et al. [1] made a partial classi cation of Calabi-Yau manifolds in WP4. An approximate symmetry was found in the collection of Calabi-Yau manifolds under the interchange of  \chi and - \chi. The goal of this thesis is to construct Calabi-Yau manifolds in this class and see if it is possible to extend the list made in[1]. Motivation behind this project is a symmetry of string theory called mirror symmetry that predicts a perfect symmetry in all Calabi-Yau manifolds when interchanging  \chi and - \chi. We find a way to extend the results of[1] but also come to the conclusion that a complete classi cation of orbifolds in
weighted projective space has already been made in[2],[4]. We will also discuss these results.

Publication date: 
July, 2012