Aut(X, σ) and Aut(X/σ) are not isomorphic in the category of surfaces with nodes

Abstract

A symmetric Riemann surface is a pair (X, σ) where X is a Riemann surface and σ is an anticonformal involution. We denote by Aut(X, σ) the subgroup of Aut(X) defined by the automorphisms commuting with σ. There is a natural isomorphism between Aut(X, σ) and Aut(X/σ). In this article we shall show that this isomorphism does not stand if X is a Riemann surface with nodes.

Keywords:

• Automorphism of surfaces
• Surfaces with nodes
• Symmetric Riemann surfaces with nodes and Klein surfaces with nodes
• AMS Subject Classifications: 30F50
• 30F10

Notes

Email: [email protected]

Additional information

Notes on contributors

Ignacio C. Garijo *

Email: [email protected]