The versal deformation of cyclic quotient singularities

TL;DR

This paper characterizes the versal deformation of 2D cyclic quotient singularities using combinatorial structures like dots in a triangle and rooted trees, providing explicit equations for these deformations.

Contribution

It introduces a novel combinatorial approach to describe the equations governing the versal deformation of cyclic quotient singularities.

Findings

Equations for reduced components are determined by systems of dots in a triangle.

The equations of the versal deformation are governed by rooted trees.

Provides explicit combinatorial descriptions for deformation equations.

Abstract

We describe the versal deformation of two-dimensional cyclic quotient singularities in terms of equations, following Arndt, Brohme and Hamm. For the reduced components the equations are determined by certain systems of dots in a triangle. The equations of the versal deformation itself are governed by a different combinatorial structure, involving rooted trees.