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<p>Clemens’ conjecture states that 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.</p>

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Periods of families of curves in threefolds

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月31日

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  • Hossein Movasati

摘要

Clemens’ conjecture states that 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.