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arXiv · 2610.00189

A characterization of the Ree curve

Saeed Tafazolian
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Abstract

Let $q=3q_0^2$, where $q_0=3^s$ and $s\ge3$. We prove that a smooth, projective, geometrically irreducible curve over $\F_q$ with $q^3+1$ rational points and genus \[ \frac32q_0(q-1)(q+q_0+1) \] is $\F_q$-isomorphic to the Ree curve.

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Saeed Tafazolian. 2026-10-02. A characterization of the Ree curve. https://arxiv.org/abs/2610.00189

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