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Résumé |
Recently, as part of a project to find CY manifolds for which both the Hodge numbers ($h^{11}, h^{21}$) are small, manifolds have been found with Hodge numbers (4,1) and (1,1). The one-dimensional special geometries of their complex structures are more complicated than those previously studied. I will review these, emphasising the role of the fundamental period and Picard-Fuchs equation.
Two arithmetic aspects arise: the first is the role of $\zeta(3)$ in the monodromy matrices and the second is the fact, perhaps natural to a number theorist, that through a study of the CY manifolds over finite fields, modular functions can be associated to the singular manifolds of the family. |
