Pfaffian Calabi-Yau Threefolds and Mirror Symmetry

TL;DR

This paper advances the understanding of mirror symmetry for non-complete intersection Calabi-Yau threefolds by constructing new examples and analyzing their mirror families through period integrals and Picard-Fuchs equations.

Contribution

It constructs four new smooth non-complete intersection Calabi-Yau threefolds with h^{1,1}=1 and computes their mirror period integrals, confirming expected mirror symmetry properties.

Findings

Constructed four new non-complete intersection Calabi-Yau threefolds.

Computed period integrals matching predicted mirror symmetry equations.

Identified mirror families with multiple maximally unipotent monodromy points.

Abstract

The aim of this article is to report on recent progress in understanding mirror symmetry for some non-complete intersection Calabi-Yau threefolds. We first construct four new smooth non-complete intersection Calabi-Yau threefolds with h^{1,1}=1, whose existence was previously conjectured by C. van Enckevort and D. van Straten. We then compute the period integrals of candidate mirror families of F. Tonoli's degree 13 Calabi-Yau threefold and three of the new Calabi-Yau threefolds. The Picard-Fuchs equations coincide with the expected Calabi-Yau equations. Some of the mirror families turn out to have two maximally unipotent monodromy points.