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arXiv · 1804.05643

Rational curves on cubic hypersurfaces over finite fields

Adelina Mânzăţeanu
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Abstract

Given a smooth cubic hypersurface $X$ over a finite field of characteristic greater than 3 and two generic points on $X$, we use a function field analogue of the Hardy-Littlewood circle method to obtain an asymptotic formula for the number of degree $d$ rational curves on $X$ passing through those two points. We use this to deduce the dimension and irreducibility of the moduli space parametrising such curves, for large enough $d$.

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Adelina Mânzăţeanu. 2018-04-16. Rational curves on cubic hypersurfaces over finite fields. https://arxiv.org/abs/1804.05643

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