Frobenius polynomials for Calabi-Yau equations

TL;DR

This paper presents a modified Dwork's method to compute Frobenius polynomials for Calabi-Yau families, linking them to holomorphic periods near special monodromy points, with practical examples.

Contribution

It introduces a variation of Dwork's unit-root method tailored for degree four Frobenius polynomials in Calabi-Yau families, enhancing computational techniques.

Findings

Successfully computes Frobenius polynomials for specific Calabi-Yau examples.

Connects Frobenius polynomials to holomorphic periods at maximal unipotent monodromy.

Provides illustrative examples demonstrating the method's effectiveness.

Abstract

We describe a variation of Dworks unit-root method to determine the degree four Frobenius polynomial for members of a 1-modulus Calabi-Yau family over $\mathbb{P}^1$ in terms of the holomorphic period near a point of maximal unipotent monodromy. The method is illustrated on a couple of examples.