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Moduli and periods of elliptic surfaces

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If you have a question about this talk, please contact Dhruv Ranganathan .

The moduli space of elliptic surfaces is framed by rank 1 foliations along each of which the derivative of the period map can be described in terms of certain differentials of the second kind. These forms provide a basis of the appropriate part of the cohomology of the surface and can be used to prove a generic Torelli theorem and an infinitesimal Schottky theorem. We give an explicit formula for the cup product of these forms, analogous to Riemann’s bilinear relation in the 1-dimensional context, and extract explicit co-ordinates on the moduli space from this picture.

This talk is part of the Algebraic Geometry Seminar series.

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