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Web page: Alexandru I. Suciu | Created: September 17, 2001 |
| Maintained by: Misha Kogan | URL: http://www.math.neu.edu/~GASC/gas/verrill.html |
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| The intermediate Jacobian of certain rigid Calabi-Yau threefolds |
Helena Verrill
(Universitaet Hannover)
| Abstract: A rigid Calabi-Yau threefold X has 2 dimensional middle cohomology, so the intermediate Jacobian H^{3,0}(X,C)/H_3(X,Z) is a elliptic curve with period lattice given by the periods of the holomorphic 3 form integrated against the 3 cycles on X. I will look at the cases where X is defined over Q and is obtained as a fibre product of a family of elliptic curves over a modular curve. Chad Schoen described the 6 cases where this construction gives a rigid Calabi-Yau threefold. I will show how to describe the 3 cycles explicitly in terms of modular symbols, which allows a numerical computation of the period lattice. I will also describe the relationship between the periods and the L-series of the middle cohomology, and the monodromy of the fibration. |
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Web page: Alexandru I. Suciu | Created: September 17, 2001 |
| Maintained by: Misha Kogan | URL: http://www.math.neu.edu/~GASC/gas/verrill.html |