Resolution of Orbifold Singularities in String Theory

TL;DR

This paper reviews how orbifold singularities are resolved in string theory, focusing on the relationship between classical geometric resolutions and string-theoretic descriptions, especially for abelian quotient singularities.

Contribution

It introduces a method for analyzing local quotients of the form C^d/G with G abelian, utilizing mirror symmetry to study the moduli space of resolutions.

Findings

Explicit analysis of C^2/Z_n singularities

Connection between classical and string resolutions

Use of mirror symmetry in moduli space analysis

Abstract

In this paper the relationship between the classical description of the resolution of quotient singularities and the string picture is reviewed in the context of N=(2,2) superconformal field theories. A method for the analysis of quotients locally of the form C^d/G where G is abelian is presented. Methods derived from mirror symmetry are used to study the moduli space of the blowing-up process. The case C^2/Z_n is analyzed explicitly. This is largely a review paper to appear in "Essays on Mirror Manifolds, II".