Pfaffian Calabi-Yau Threefolds and Mirror Symmetry

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.

30 pages, to appear in Communications in Number Theory and Physics

References in corpus (6)

• Families of Quintic Calabi-Yau 3-Folds with Discrete Symmetries
• Higher genus Gromov-Witten invariants of the Grassmannian, and the Pfaffian Calabi-Yau threefolds
• Open mirror symmetry for Pfaffian Calabi-Yau 3-folds
• Quantum cohomology of a Pfaffian Calabi-Yau variety: verifying mirror symmetry predictions
• Pfaffian Calabi-Yau threefolds, Stanley-Reisner schemes and mirror symmetry
• Mirror symmetry and tropical geometry