What question did this study set out to answer?

To construct a method for resolving type D4 surface singularities using geometric invariant theory.

January 22, 2026Open Access

The McKay correspondence in type D4 via variation of geometric invariant theory

TATarig AbdelgadirLoughborough University ESEd SegalUniversity College London

Key Points

To construct a method for resolving type D4 surface singularities using geometric invariant theory.
Utilized explicit geometric invariant theory construction.
Developed both minimal and orbifold resolutions.
Employed a Tannakian approach suitable for larger groups.
Achieved a minimal resolution of the type D4 surface singularity.
Obtained an orbifold resolution through the construction.
Demonstrated applicability to a broader class of geometric problems.

Abstract

Abstract We present an explicit geometric invariant theory construction which produces both the minimal resolution of the type D₄ surface singularity, and also the orbifold resolution. Our construction is based on a Tannakian approach which is in principle applicable to larger groups.

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