Plane maximal curves (Q2717624)

In the paper under review, maximal nonsingular plane curves defined over a finite field with \(q^2\) elements are studied. A maximal curve is defined to be a curve such that the number of its rational points attains the Hasse-Weil bound. The authors prove that the degree \(d\) of such a curve is either \(d=q+1\) or \(2d\leq q+2\) if \(q>5\). In the former case the curve is the well-known Hermitian curve. Then, they study the classicality and Frobenius classicality for the linear system cut out by lines. Finally, they prove that a Hurwitz curve is maximal if and only if it is covered by the Hermitian curve.