PreprintCC BY 4.0arXiv
Associated Varieties of Finite-Group Orbifolds
Abstract
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 $R_{V^G}\longrightarrow (R_V)^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.
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BibTeX
@misc{riesen2026associated,
title = {{Associated Varieties of Finite-Group Orbifolds}},
author = {Andrew Riesen},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03611},
eprint = {2611.03611},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03611},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Associated Varieties of Finite-Group Orbifolds
AU - Andrew Riesen
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03611
UR - https://arxiv.org/abs/2611.03611
AB - 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 X_V^G≅ 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 C_2-quotient, which also implies that V^G is strongly finitely generated. Consequently, quasi-lisseness and C_2-cofiniteness descend to finite-group orbifolds, and hence, by existing results, so does strong rationality.
ER -