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arXiv · 2202.08677

Periods of families of curves in threefolds

Hossein Movasati
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Abstract

Clemens' conjecture states that the the number of rational curve in a generic quintic threefold is finite. If it is false we prove that certain periods of rational curves in such a quintic threefold must vanish. Our method is based on a generalization of a proof of Max Noether's theorem using infinitesimal variation of Hodge structures and its reformulation in terms of integrals and Gauss-Manin connection.

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Hossein Movasati. 2022-02-17. Periods of families of curves in threefolds. https://arxiv.org/abs/2202.08677

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