Pfaffian Calabi-Yau Threefolds and Mirror Symmetry
Algebraic Geometry
2013-01-14 v4 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.1006.0223,
title = {Pfaffian Calabi-Yau Threefolds and Mirror Symmetry},
author = {Atsushi Kanazawa},
journal= {arXiv preprint arXiv:1006.0223},
year = {2013}
}
Comments
30 pages, to appear in Communications in Number Theory and Physics