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Monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds
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Yao-Han Chen
Published/Copyright:
May 13, 2008
Abstract
In this paper we are concerned with the monodromy of Picard-Fuchs 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 and whose levels are related to the geometric invariants of the Calabi-Yau threefolds.
Received: 2006-05-29
Revised: 2007-01-15
Published Online: 2008-05-13
Published in Print: 2008-March
© Walter de Gruyter
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Articles in the same Issue
- Smooth localized parametric resonance for wave equations
- Estimates and regularity results for the DiPerna-Lions flow
- Sur le nombre d'éléments exceptionnels d'une base additive
- Alder's conjecture
- Local monotonicity and mean value formulas for evolving Riemannian manifolds
- Projective-injective modules, Serre functors and symmetric algebras
- Monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds
- Zeros of complex caloric functions and singularities of complex viscous Burgers equation
- Generalised form of a conjecture of Jacquet and a local consequence
