A lecture on Arithmetic Mirror Symmetry and Calabi-Yau manifolds
Abstract
We extend our variant of mirror symmetry for K3 surfaces \cite{GN3} and clarify its relation with mirror symmetry for Calabi-Yau manifolds. We introduce two classes (for the models A and B) of Calabi-Yau manifolds fibrated by K3 surfaces with some special Picard lattices. These two classes are related with automorphic forms on IV type domains which we studied in our papers \cite{GN1}-\cite{GN6}. Conjecturally these automorphic forms take part in the quantum intersection pairing for model A, Yukawa coupling for model B and mirror symmetry between these two classes of Calabi-Yau manifolds. Recently there were several papers by physicists where it was shown on some examples. We propose a problem of classification of introduced Calabi-Yau manifolds. Our papers \cite{GN1}-\cite{GN6} and \cite{N3}-\cite{N14} give a hope that this is possible. They describe possible Picard or transcendental lattices of general K3 fibers of the Calabi-Yau manifolds.
Cite
@article{arxiv.alg-geom/9612002,
title = {A lecture on Arithmetic Mirror Symmetry and Calabi-Yau manifolds},
author = {Valeri A. Gritsenko and Viacheslav V. Nikulin},
journal= {arXiv preprint arXiv:alg-geom/9612002},
year = {2014}
}
Comments
AMS-Tex, 11 pages, no figures. The variant prepared for publication; many small changes introduced