PreprintarXiv licencearXiv
A characterization of the Ree curve
Abstract
Let q=3q02, where q0=3s and s≥3. We prove that a smooth, projective, geometrically irreducible curve over Fq with q3+1 rational points and genus 3/2q0(q−1)(q+q0+1) is Fq-isomorphic to the Ree curve.
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BibTeX
@misc{tafazolian2026characterization,
title = {{A characterization of the Ree curve}},
author = {Saeed Tafazolian},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00189},
eprint = {2610.00189},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00189},
}
RIS
TY - UNPB
TI - A characterization of the Ree curve
AU - Saeed Tafazolian
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.00189
UR - https://arxiv.org/abs/2610.00189
AB - Let q=3q_0^2, where q_0=3^s and s≥3. We prove that a smooth, projective, geometrically irreducible curve over F_q with q^3+1 rational points and genus 3/2q_0(q−1)(q+q_0+1) is F_q-isomorphic to the Ree curve.
ER -