Rational curves on smooth cubic hypersurfaces over finite fields
classification
🧮 math.AG
math.NT
keywords
cubiccurvesdimensionfiniterationalsmoothcharacteristicdegree
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Let k be a finite field with characteristic exceeding 3. We prove that the space of rational curves of fixed degree on any smooth cubic hypersurface over k with dimension at least 11 is irreducible and of the expected dimension.
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