nLab
ADE singularity

Contents

Idea

An ADE singularity is a orbifold fixed point locally of the form 2/Γ\mathbb{C}^2/\Gamma with ΓSU(2)\Gamma \hookrightarrow SU(2) a finite subgroup of the special unitary group given by the ADE classification (and SU(2)SU(2) is understood with its defining linear action on the complex vector space 2\mathbb{C}^2).

ADE 2Cycle

These singularities have crepant resolutions, obtained by repeatedly blowing up at singular points. The resulting exceptional fiber (the blow-up of the singular point, an ALE space) is a union of Riemann spheres that touch each other such as to form the shape of the corresponding Dynkin diagram.

(graphics grabbed from Wijnholt 14, part III)

References

General

Families of examples of G2 orbifolds with ADE singularities are constructed in

In the context of string compactifications

See also at F-branes -- table

Revised on December 18, 2015 16:21:47 by Urs Schreiber (195.37.209.180)