The moduli space of Type~A surfaces with torsion and non-singular symmetric Ricci tensor

TL;DR

This paper studies the structure of moduli spaces of Type A surface connections, focusing on how the signature of the symmetric Ricci tensor affects their smoothness and singularities.

Contribution

It characterizes the moduli spaces of Type A connections on surfaces, revealing conditions under which they are smooth or contain orbifold singularities based on Ricci tensor signature.

Findings

Moduli spaces are smooth for Ricci tensor signatures (1,1) or (0,2).

Orbifold singularities occur in moduli spaces when the Ricci tensor signature is (2,0).

The analysis applies to both oriented and unoriented surfaces.

Abstract

We examine the moduli spaces of Type~A connections on oriented and unoriented surfaces both with and without torsion in relation to the signature of the associated symmetric Ricci tensor. If the signature of the symmetric Ricci tensor is (1,1) or (0,2), the moduli spaces are smooth. If the signature is (2,0), there is an orbifold singularity.