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arXiv · 2604.26556

Rational curves on cubic hypersurfaces in positive characteristic

Natsume Kitagawa
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Abstract

We study the moduli spaces of rational curves on cubic hypersurfaces in characteristic $\neq2,3$. As a result, we prove that for every integer $d\geq1$ the Kontsevich moduli space of stable maps on a smooth cubic hypersurface $X$ of degree $d$ is irreducible if the dimension of $X$ is greater than or equal to $4$.

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Natsume Kitagawa. 2026-04-29. Rational curves on cubic hypersurfaces in positive characteristic. https://arxiv.org/abs/2604.26556

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