Ordinary Calabi-Yau-3 Crystals
Abstract
We show that crystals with the properties of crystalline cohomology of ordinary Calabi-Yau threefolds in characteristic p>0, exhibit a remarkable similarity with the well known structure on the cohomology of complex Calabi-Yau threefolds near a boundary point of the moduli space with maximal unipotent local monodromy. In particular, there are canonical coordinates and an analogue of the prepotential of the Yukawa coupling. Moreover we show p-adic analogues of the integrality properties for the canonical coordinates and the prepotential of the Yukawa coupling, which have been observed in the examples of Mirror Symmetry.
Cite
@article{arxiv.math/0212061,
title = {Ordinary Calabi-Yau-3 Crystals},
author = {Jan Stienstra},
journal= {arXiv preprint arXiv:math/0212061},
year = {2007}
}
Comments
17 p.; Latex2e;v2: only change: style file fic-l.cls provided; to appear in proceedings of Workshop on Calabi-Yau Varieties and Mirror Symmetry at Fields Institute, July 2001