Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-12-03
Commun.Math.Phys. 210 (2000) 1-11
Physics
High Energy Physics
High Energy Physics - Theory
AMS-Tex, 11 pages, no figures. The variant prepared for publication; many small changes introduced
Scientific paper
10.1007/s002200050769
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.
Gritsenko Valeri A.
Nikulin Viacheslav V.
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