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March 2019 Rational curves on a smooth Hermitian surface
Norifumi Ojiro
Hiroshima Math. J. 49(1): 161-173 (March 2019). DOI: 10.32917/hmj/1554516042

Abstract

We study the set $R$ of nonplanar rational curves of degree $d \lt q + 2$ on a smooth Hermitian surface $X$ of degree $q + 1$ defined over an algebraically closed field of characteristic $p > 0$, where $q$ is a power of $p$. We prove that $R$ is the empty set when $d \lt q + 1$. 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.

Citation

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Norifumi Ojiro. "Rational curves on a smooth Hermitian surface." Hiroshima Math. J. 49 (1) 161 - 173, March 2019. https://doi.org/10.32917/hmj/1554516042

Information

Received: 18 July 2018; Revised: 1 February 2019; Published: March 2019
First available in Project Euclid: 6 April 2019

zbMATH: 07090068
MathSciNet: MR3936652
Digital Object Identifier: 10.32917/hmj/1554516042

Subjects:
Primary: 14M99, 51E20
Secondary: 14N99

Rights: Copyright © 2019 Hiroshima University, Mathematics Program

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Vol.49 • No. 1 • March 2019
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