Chapter

Calabi-Yau Varieties: Arithmetic, Geometry and Physics

Volume 34 of the series Fields Institute Monographs pp 503-539

Introduction to Arithmetic Mirror Symmetry

  • Andrija PeruničićAffiliated withDepartment of Mathematics and Statistics, Queen’s University Email author 

* Final gross prices may vary according to local VAT.

Get Access

Abstract

We describe how to find period integrals and Picard-Fuchs differential equations for certain one-parameter families of Calabi-Yau manifolds. These families can be seen as varieties over a finite field, in which case we show in an explicit example that the number of points of a generic element can be given in terms of p-adic period integrals. We also discuss several approaches to finding zeta functions of mirror manifolds and their factorizations. These notes are based on lectures given at the Fields Institute during the thematic program on Calabi-Yau Varieties: Arithmetic, Geometry, and Physics.