Associated Varieties of Finite-Group Orbifolds

Let V be a simple, strongly finitely generated vertex algebra with a connected nonnegative integer grading, and let G be a finite group of grading-preserving automorphisms. In this paper, we prove that XVG XV/G as reduced Poisson varieties. More precisely, the canonical surjection RVG (RV)G has nilpotent kernel. The proof uses a uniform derivative bound in a relative C₂-quotient, which also implies that VG is strongly finitely generated. Consequently, quasi-lisseness and C₂-cofiniteness descend to finite-group orbifolds, and hence, by existing results, so does strong rationality.