Infinite-dimensional Lie algebras and the period map for curves

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We compute higher-order differentials of the period map for curves and show how they factor through the corresponding higher Kodaira-Spencer classes. Our approach is based on the infinitesimal equivariance of the period map, due to Arbarello and De Concini \cite{AD}.
36 pages, LaTeX. This corrects a reference in the earlier version

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