Smooth embeddings for the Suzuki and Ree curves

Abdulla Eid, Iwan Duursma

Research output: Chapter in Book/Report/Conference proceedingChapter


The Hermitian, Suzuki and Ree curves form three special families of curves with unique properties. They arise as the Deligne-Lusztig varieties of dimension one and their automorphism groups are the algebraic groups of type 2A2, 2B2 and 2G2, respectively. For the Hermitian and Suzuki curves very ample divisors are known that yield smooth projective embeddings of the curves. In this paper we establish a very ample divisor for the Ree curves. Moreover, for all three families of curves we find a symmetric set of equations for a smooth projective model, in dimensions 2, 4 and 13, respectively. Using the smooth model we determine the unknown non-gaps in the Weierstrass semigroup for a rational point on the Ree curve.

Original languageEnglish (US)
Title of host publicationAlgorithmic arithmetic, geometry, and coding theory
EditorsStéphane Ballet, Marc Perret, Alexey Zaytsev
PublisherAmerican Mathematical Society
Number of pages41
ISBN (Electronic)9781470423391
ISBN (Print)9781470414610
StatePublished - 2015

Publication series

NameContemporary Mathematics
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

ASJC Scopus subject areas

  • General Mathematics


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