Weierstrass points on certain non-classical curves
type: Item
instance of: scholarly article
title: Weierstrass points on certain non-classical curves
zbMATH Open document ID: 0575.14014
DOI: 10.1007/BF01200462
author: Arnaldo Garcia
author: Paulo Henrique Viana
published in: Archiv der Mathematik
publication date: 1986-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 14H55
Mathematics Subject Classification ID: 14H45
zbMATH DE Number: 3918536
zbMATH Keywords: non classical gap sequence
zbMATH Keywords: Weierstrass points
MaRDI profile type: Publication
cites work: Die Wronskische Determinante in beliebigen differenzierbaren Funktionenkörpern
cites work: Zur arithmetischen Theorie der algebraischen Funktionen. II: Allgemeine Theorie der Weierstraßpunkte
cites work: Über die Automorphismengruppe eines algebraischen Funktionenkörpers von Primzahlcharakteristik. II: Ein spezieller Typ von Funktionenkörpern
full work available at URL: https://doi.org/10.1007/bf01200462
OpenAlex ID: W2061094055
description: scientific article; zbMATH DE number 3918536