Séminaire "Equations différentielles"
Abstract : Elliptic surfaces form a distinguished class in the Enriques--Kodaira classification of complex surfaces. The derivative of the period map for the weight 2 Hodge structure of these surfaces contains enough projective information to recover the base curve; this leads to a generic Torelli theorem for Jacobian surfaces (those with a section). On the way we obtain also a new view of the cohomology of these surfaces; for example, rational elliptic surfaces each possess a naturally defined period matrix, up to a finite group action.
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Vasily Golyshev & Vladimir Roubtsov