On Curves Covered by the Hermitian Curve

Caps on Hermitian varieties and maximal curves

“…Example 4.7 ([6, §6]) A similar but non-isomorphic example is given in [6]. Again, assume that q ≡ 2 (mod 3).…”

Quotient curves of the Suzuki curve

“…In particular, by means of quotient curves of X , the genus and plane models of a huge number of maximal curves were found; see e.g. [7], [3] and [4].…”

“…The approach employed in this paper is similar to that in [3] and [4]: a concrete realization of S in P 4 is stated via a very ample complete linear series obtained from the enumerator of its Zeta function (cf. Section 3); this embedding is such that Sz(q) acts linearly on S (cf.…”

A new family of maximal curves over a finite field

“…Apparently, the known maximal curves are all Galois F q 2 -covered by one of the curves below, see [1,2,3,4,5,6,7,8,15,16,17,18,19,20,21,22,28,29].…”