Free curves in Fano hypersurfaces must have high degree
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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