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<p>A general hypersurface <i>X</i> of degree at most <i>n</i> in projective (<i>n</i> + 1)-space contains curves <i>C</i> of any genus <i>g</i> ≥ 0 and sufficiently large degree depending on <i>g</i> whose normal and conormal bundles in <i>X</i> have good postulation or natural cohomology in a sense that each twist has either <i>H</i><sup>0</sup> = 0 or <i>H</i><sup>1</sup> = 0<i>.</i> This implies a polarized version of the interpolation property for <i>C</i> on <i>X.</i></p>

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Polarized Interpolation and Normal Postulation for Curves on Fano Hypersurfaces

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • Ziv Ran

摘要

A general hypersurface X of degree at most n in projective (n + 1)-space contains curves C of any genus g ≥ 0 and sufficiently large degree depending on g whose normal and conormal bundles in X have good postulation or natural cohomology in a sense that each twist has either H0 = 0 or H1 = 0. This implies a polarized version of the interpolation property for C on X.