Séminaire de Mathématique

Moduli and Periods of Elliptic Surfaces

by Nicholas Shepherd-Barron (King’s College London)

Europe/Paris
Centre de conférences Marilyn et James Simons (IHES)

Centre de conférences Marilyn et James Simons

IHES

Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette
Description

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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