Browsing by Author "Yui, Noriko"

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Differential equations satisfied by modular forms and K3 surfaces
(2007-06-01)
Yang, Yifan
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Yui, Noriko
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應用數學系
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Department of Applied Mathematics
We study differential equations satisfied by modular forms of two variables associated to Gamma(1) x Gamma(2), where Gamma(i) (i = 1, 2) are genus zero subgroups of SL2(R) commensurable with SL2(Z), e.g., Gamma(0)(N) or Gamma(0)(N)* for some N. In some examples, these differential equations are realized as the Picard-Fuchs differential equations of families of K3 surfaces with large Picard numbers, e.g., 19,18,17,16. Our method rediscovers some of the Lian-Yau examples of "modular relations" involving power series solutions to the second and the third order differential equations of Fuchsian type in [14], [15].
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.