Infinitely many Riemann surfaces with transitive action on Weierstrass points

TL;DR

This paper proves the existence of infinitely many non-hyperelliptic Riemann surfaces with automorphism groups acting transitively on Weierstrass points and classifies those with simple automorphism groups.

Contribution

It establishes the existence of infinitely many such surfaces and classifies all simple cases, advancing understanding of symmetries in Riemann surfaces.

Findings

Infinitely many non-hyperelliptic Riemann surfaces with transitive automorphism action on Weierstrass points.

Complete classification of simple automorphism group cases.

Automorphism groups acting transitively on Weierstrass points in these surfaces.

Abstract

In this short note, we prove the existence of infinitely many pairwise non-isomorphic non-hyperelliptic Riemann surfaces with automorphism group acting transitively on the Weierstrass points. We also found all those compact Riemann surfaces with automorphism group acting transitively on the Weierstrass points, under the assumption that they are simple.