The Deligne-Lusztig varieties associated to the Coxeter classes of the algebraic groups A2, B2 and G2 are affine algebraic curves. We produce explicit projective models of the closures of these curves. Furthermore for d the Coxeter number of these groups, we find polynomials for each of these models that cut out the Fq-points, the Fqd -points and the Fqd+1… (More)