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The McKay correspondence in type $D_4$ via VGIT

Tarig Abdelgadir, Ed Segal

Abstract

We present an explicit GIT construction which produces both the minimal resolution of the type $D_4$ surface singularity, and also the orbifold resolution. Our construction is based on a Tannakian approach which is in principle applicable to arbitrary quotient singularities.

The McKay correspondence in type $D_4$ via VGIT

Abstract

We present an explicit GIT construction which produces both the minimal resolution of the type surface singularity, and also the orbifold resolution. Our construction is based on a Tannakian approach which is in principle applicable to arbitrary quotient singularities.
Paper Structure (3 sections, 6 theorems, 63 equations, 1 table)

This paper contains 3 sections, 6 theorems, 63 equations, 1 table.

Table of Contents

  1. Introduction
  2. The Tannakian approach
  3. The construction

Key Result

Theorem 3.4

Let $\vartheta$ be the character $(1,1,1,1)$.

Theorems & Definitions (20)

  • Remark 1.1
  • Remark 1.2
  • Remark 1.3
  • Remark 2.1
  • Example 2.2
  • Example 2.3
  • Remark 3.2
  • Remark 3.3
  • Theorem 3.4
  • Lemma 3.5
  • ...and 10 more