Ordinary Calabi-Yau-3 Crystals

Details Ordinary Calabi-Yau-3 Crystals Ordinary Calabi-Yau-3 Crystals

2002-12-04

arxiv.org/abs/math/0212061v2

Mathematics

Algebraic Geometry

17 p.; Latex2e;v2: only change: style file fic-l.cls provided; to appear in proceedings of Workshop on Calabi-Yau Varieties an

Scientific paper

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.

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