Transitivity on Weierstrass points

TL;DR

This paper investigates the symmetry properties of Riemann surfaces by examining how their automorphism groups act on Weierstrass points, focusing on specific classes like hyperelliptic surfaces, PSL(2, q) automorphism groups, Platonic surfaces, and Fermat curves.

Contribution

It characterizes Riemann surfaces with automorphism groups acting transitively on Weierstrass points within several important classes of surfaces.

Findings

Identifies conditions for transitivity on Weierstrass points

Classifies surfaces with specific automorphism groups acting transitively

Provides new insights into symmetry properties of special Riemann surfaces

Abstract

We look for Riemann surfaces whose automorphism group acts transitively on the Weierstrass points. We concentrate on hyperelliptic surfaces, surfaces with PSL(2, q) as automorphism group, Platonic surfaces and Fermat curves.