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

The Deligne–Lusztig varieties associated to the Coxeter classes of the algebraic groups ${^{2}A}_2,{^{2}B}_2$, and ${^{2}G}_2$ 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 ${\BBF}_q$-points, the ${\BBF}_{q^d}$-points, and the ...