Monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds

Details Monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds Monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds

2006-05-26

arxiv.org/abs/math/0605675v3

Mathematics

Algebraic Geometry

32 pages References added

Scientific paper

In this paper we are concerned with the monodromy of Picard-Fuch differential equations associated with one-parameter families of Calabi-Yau threefolds. Our results show that in the hypergeometric cases the matrix representations of monodromy relative to the Frobenius bases can be expressed in terms of the geometric invariants of the underlying Calabi-Yau threefolds. This phenomenon is also verified numerically for other families of Calabi-Yau threefolds in the paper. Furthermore, we discover that under a suitable change of bases the monodromy groups are contained in certain congruence subgroups of Sp(4,Z) of finite index whose levels are related to the geometric invariants of the Calabi-Yau threefolds

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