Notes on Calabi-Yau ordinary differential equations

TL;DR

This paper explores the structure of Calabi-Yau differential equations and their connection to the arithmetic properties of Calabi-Yau varieties, clarifying previous observations and computations.

Contribution

It offers new insights into the relationship between Calabi-Yau differential equations and the arithmetic of associated varieties, enhancing understanding of their underlying structures.

Findings

Clarified the relation between Calabi-Yau equations and arithmetic properties

Provided explanations for recent computational observations

Connected differential equations with geometric structures

Abstract

We investigate the structures of Calabi-Yau differential equations and the relations to the arithmetic of the pencils of Calabi-Yau varieties behind the equations. This provides explanations of some observations and computations in a recent paper by Samol and van Straten.