1006.0223 (Atsushi Kanazawa)

Pfaffian Calabi-Yau Threefolds and Mirror Symmetry    [PDF]

Atsushi Kanazawa

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 Calabi-Yau threefolds with $h^{1,1}=1$ of non-complete intersection type, whose existence was previously conjectured by C. van Enckevort and D. van Straten. We then compute the period integral of candidate mirror families for these Calabi-Yau threefolds and check that the Picard-Fuchs equations coincide with the expected Calabi-Yau equations listed in their papers. Some of the mirror families turn out to have two maximally unipotent monodromy points.

View original: http://arxiv.org/abs/1006.0223