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The Deligne-Lusztig varieties associated to the Coxeter classes of thealgebraic groups 2A2, 2B2 and 2G2 are affine algebraic curves. We produceexplicit projective models of the closures of these curves. Furthermore for $d$the Coxeter number of these groups, we find polynomials for each of thesemodels that cut out the $\F_q$-points, the $\F_{q^d}$-points and the$\F_{q^{d+1}}$-points, and demonstrate a relation satisfied by thesepolynomials.

Canonical Projective Embeddings of the Deligne-Lusztig Curves Associated to $2A2$, $2B2$ and $2G2$