Weierstrass points on certain non-classical curves
We study the curves \(A(Y)=B(X)\) where A(Y) is a separable additive polynomial of degree \(p^ n>1\) (p is the characteristic of the ground field) and B(X) is a polynomial with degree not divisible by p. We determine certain families of non-classical curves of the above type and, for each member of such a family, we compute its Weierstrass points and also the sequence of order of the differentials of the first kind at any point of this member-curve. Up to genus 8 the only non-classical curves of this kind are the examples originally given by F. K. Schmidt; in genus 9, however, there are two other families of non-classical curves.
scientific article; zbMATH DE number 3918536