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arXiv · 1812.05470

Rational curves on a smooth Hermitian surface

Norifumi Ojiro
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Abstract

We study the set $R$ of nonplanar rational curves of degree $d 0$, where $q$ is a power of $p$. We prove that $R$ is the empty set when $d<q+1$. In the case where $d=q+1$, we count the number of elements of $R$ by showing that the group of projective automorphisms of $X$ acts transitively on $R$ and by determining the stabilizer subgroup. In the special case where $X$ is the Fermat surface, we present an element of $R$ explicitly.

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Norifumi Ojiro. 2019-03-08. Rational curves on a smooth Hermitian surface. https://doi.org/10.32917/hmj%2F1554516042

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