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arXiv · 2404.17341

Free curves in Fano hypersurfaces must have high degree

Raymond Cheng
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Abstract

The purpose of this note is to show that the minimal $e$ for which every smooth Fano hypersurface of dimension $n$ contains a free rational curve of degree at most $e$ cannot be bounded by a linear function in $n$ when the base field has positive characteristic. This is done by providing a super-linear bound on the minimal possible degree of a free curve in certain Fermat hypersurfaces.

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Raymond Cheng. 2024-04-26. Free curves in Fano hypersurfaces must have high degree. https://doi.org/10.1090/proc/17206

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