In this paper, we examine superspecial genus-2 curves C: y 2= x (x− 1)(x− λ)(x− μ)(x− ν) in
odd characteristic p. As a main result, we show that the difference between any two …

For an algebraic curve X defined over an algebraically closed field of characteristic p> 0, the
a-number a (X) is the dimension of the space of exact holomorphic differentials on X. We …

We characterize certain maximal curves over finite fields defined by equations of type yn= x
m+ x. Moreover, we show that a maximal curve over F q 2 defined by the affine equation yn …

We construct examples of curves defined over the finite field F q 6 which are covered by the
GK-curve. Thus such curves are maximal over F q 6 although they cannot be covered by the …

In arithmetic and algebraic geometry, superspecial (s. sp. for short) curves are one of the
most important objects to be studied, with applications to cryptography and coding theory. If …

On maximal curves of Fermat type Page 1 Adv. Geom. 13 (2013), 613–617 Advances in
Geometry DOI 10.1515 / advgeom-2013-0002 c de Gruyter 2013 On maximal curves of Fermat …

Let Fq2 be a finite field with q2 elements, where q is a prime power, and let C be a
projective, nonsingular, geometrically irreducible algebraic curve (hereafter referred to as a …

For X a curve over a field of positive characteristic, we investigate when the canonical
representation of Aut (X) on H 0 (X, Ω X) is irreducible. Any curve with an irreducible …

Full article: A note on certain maximal curves Skip to Main Content Taylor and Francis
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In the study of algebraic curves and their moduli spaces, it is important to determine the $ a $-
numbers of curves over a field of positive characteristic. It is known that non-hyperelliptic …