Weierstrass gap sequences at the ramification points of trigonal Riemann surfaces
A trigonal Riemann surface M of genus \(g\geq 5\) is of n-th kind if \(\ell (nD)=n+1\) and \(\ell (n+1)D\geq n+3\), where D is the divisor of degree 3 associated to M. Total and ordinary ramification points of M as 3-sheeted covering of \({\mathbb{P}}^ 1\) can be classified into two types [cf. \textit{M. Coppens}, Indagationes Math. 47, 245-276 (1985; Zbl 0592.14025) and J. Pure Appl. Algebra 43, 11-25 (1986; Zbl 0616.14012)]. In this article the authors give a normalized defining equation of a trigonal Riemann surface M of n-th kind, and by investigating it they determine the types of ramification points of M and show the existence of Riemann surfaces with various types of ramification points. Some estimates on the numbers of ramification points are also obtained.
scientific article; zbMATH DE number 4059564