24 research outputs found
Weierstrass semigroups on the Skabelund maximal curve
In 2017, D. Skabelund constructed a maximal curve over as
a cyclic cover of the Suzuki curve. In this paper we explicitly determine the
structure of the Weierstrass semigroup at any point of the Skabelund curve.
We show that its Weierstrass points are precisely the
-rational points. Also we show that among the Weierstrass
points, two types of Weierstrass semigroup occur: one for the
-rational points, one for the remaining
-rational points. For each of these two types its Ap\'ery set
is computed as well as a set of generators