Some Identities For Periods of Hulek-Verrill Threefolds

TL;DR

This paper investigates the periods of Hulek-Verrill Calabi-Yau threefolds, using their birational relation to elliptic surface products to compute periods numerically, providing insights into their geometric properties.

Contribution

It introduces a method to compute periods of Hulek-Verrill threefolds via elliptic surface products and verifies this numerically in multiple examples.

Findings

Numerical verification of period computations

Confirmation of birational equivalence to elliptic surface products

Insights into the geometry of Hulek-Verrill threefolds

Abstract

We study the Hulek--Verrill families of Calabi--Yau threefolds. They are birationally equivalent to fibred products of elliptic surfaces, so we expect to be able to compute periods on these threefolds by integrating products of elliptic periods over a contour on $\mathbb{P}^1$. We numerically verify this in several examples. This article was submitted to MATRIX Annals (2024) for inclusion in the proceedings of the conference "The Geometry of Moduli Spaces in String Theory", held 2--13 September 2024.