Monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds
arXiv:math/0605675
Abstract
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
arXiv comment32 pages References added
References in corpus (7)
- Considerations of One-Modulus Calabi-Yau Compactifications: Picard-Fuchs Equations, Kähler Potentials and Mirror Maps
- Arithmetic Properties of Mirror Map and Quantum Coupling
- Picard-Fuchs equations and mirror maps for hypersurfaces
- Tables of Calabi--Yau equations
- Mirror Symmetry and Integral Variations of Hodge Structure Underlying One Parameter Families of Calabi-Yau Threefolds
- Mirror Maps and Instanton Sums for Complete Intersections in Weighted Projective Space
- Rational Curves on the Space of Determinantal Nets of Conics