Calabi—Yau Manifolds and Mirror Symmetry

Abstract

This part grew out of a post-graduate level course taught at the University of Warwick in the winter of 1998. The goal was to introduce the students to some of the basic geometry of Calabi-Yau manifolds and lead into mirror symmetry. It began with a discussion of holonomy, Ricci curvature, and Yau’s proof of the Calabi conjecture, which is not included here, and then moved on to an introduction to the different tools needed to understand the mirror symmetry conjecture. It ended with a detailed working out of the example of the quintic. Because of the diverse nature of the students following the course, with varied backgrounds in both algebraic and differential geometry, I always tried to present ideas with as little technical machinery as possible. I believe this resulted in a text quite different than some of the already existing excellent sources about mirror symmetry, and the student who wishes to pursue a career in the subject is strongly urged to consult more advanced texts, especially [197] and the very thorough [44], after reading this one.