We discuss sufficient conditions for a given curve to be covered by a maximal curve with the covering being unramified; it turns out that the given curve itself will be also maximal. We relate our main result to the question of whether or not a maximal curve is covered by the Hermitian curve. We also provide examples illustrating the results. §1. Let X be a projective, geometrically irreducible...

It is known that a Mumford curve of genus g / ∈ {5, 6, 7, 8} over a non-archimedean valued field of characteristic p > 0 has at most 2 √ g( √ g+1) automorphisms. In this note, the unique family of curves which attains this bound, and their automorphism group are determined.

A lower bound for the size of a complete cap of the polar space H(n, q2) associated to the non-degenerate Hermitian variety Un is given; this turns out to be sharp for even q when n = 3. Also, a family of caps of H(n, q2) is constructed from Fq2-maximal curves. Such caps are complete for q even, but not necessarily for q odd.

The genus g of an Fq2-maximal curve satisfies g = g1 := q(q − 1)/2 or g ≤ g2 := ⌊(q − 1) /4⌊. Previously, Fq2 -maximal curves with g = g1 or g = g2, q odd, have been characterized up to Fq2 -isomorphism. Here it is shown that an Fq2 -maximal curve with genus g2, q even, is Fq2 -isomorphic to the nonsingular model of the plane curve ∑t i=1 y q/2 = x, q = 2, provided that q/2 is a Weierstrass non...