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Associated Varieties of Finite-Group Orbifolds

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Contributed by Andrew Riesen

Version 3 / Oct 29, 2026 / CC BY 4.0

Abstract

Let VV be a simple, strongly finitely generated vertex algebra with a connected nonnegative integer grading, and let GG be a finite group of grading-preserving automorphisms. In this paper, we prove that XVG≅XV/GX_{V^G}\cong X_V/G as reduced Poisson varieties. More precisely, the canonical surjection $ R_{V^G}\longrightarrow (R_V)^G $ has nilpotent kernel. The proof uses a uniform derivative bound in a relative C2C_2-quotient, which also implies that VGV^G is strongly finitely generated. Consequently, quasi-lisseness and C2C_2-cofiniteness descend to finite-group orbifolds, and hence, by existing results, so does strong rationality.

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Version history

  1. v1Submitted by Andrew RiesenInitial depositSupersededOct 29, 2026
  2. v2Submitted by Andrew RiesenSubmitted as a new versionSupersededOct 30, 2026
  3. v3Submitted by Andrew RiesenSubmitted as a new versionCurrentNov 02, 2026