2013/11/08 by Abdulla Eid, Eid, Abdulla, Iwan Duursma +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Geometry and complex manifolds #math.AG
paper · pdf · doi:10.48550/arxiv.1311.1999
Submitted to the proceedings of the conference on Arithmetic, Geometry and Coding Theory (AGCT 2013). 40 Pages, 15 Tables, 12 Figure
arxiv created 2013/11/08 · arxiv updated 2013/11/11
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 nongaps in the Weierstrass semigroup for a rational point on the Ree curve.