Browsing by Author "Chen, Yao-Han"

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CUSPIDAL Q-RATIONAL TORSION SUBGROUP OF J(Gamma) OF LEVEL P
(2011-06-01)
Chen, Yao-Han
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應用數學系
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Department of Applied Mathematics
For p > 3 an odd prime, let Gamma be a congruence subgroup between Gamma(1)(p) and Gamma(0)(p). In this article, we give an explicit basis for the group of modular units on X(Gamma) that have divisors defined over Q. As an application, we determine the order of the cuspidal Q-rational torsion subgroup of J(Gamma) generated by the divisor classes of cuspidal divisors of degree 0 defined over Q.
Monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds
(2008-03-01)
Chen, Yao-Han
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Yang, Yian
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Yui, Noriko
;
Erdenberger, Cord
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應用數學系
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.