Topological Invariants and Moduli Spaces of Gorenstein Quasi-Homogeneous Surface Singularities

TL;DR

This paper characterizes the connected components of the space of hyperbolic Gorenstein quasi-homogeneous surface singularities, showing each component is homeomorphic to a quotient of Euclidean space by a discrete group.

Contribution

It provides a complete description of the topology of the moduli space of these surface singularities, linking topological invariants to geometric structures.

Findings

All connected components are homeomorphic to quotients of R^d by discrete groups.

The structure of the moduli space is explicitly described.

Connected components correspond to specific topological invariants.

Abstract

We describe all connected components of the space of hyperbolic Gorenstein quasi-homogeneous surface singularities. We prove that any connected component is homeomorphic to a quotient of R^d by a discrete group.