{"id":"hexagon/2610.00636","pdf":"https://hexagonmath.org/pdf/2610.00636v1","url":"https://hexagonmath.org/abs/2610.00636v1","tags":["msc:17B69"],"score":0,"title":"$C_2$-cofiniteness of finite-group orbifolds","domain":"math.QA","origin":"ai-generated","source":"hexagon","authors":["Andrew Riesen"],"reviews":0,"subject":"math.QA","summary":"Let $V$ be a simple vertex algebra with a connected nonnegative integer grading, and let $G$ be a finite group of grading-preserving automorphisms. We prove that $C_2$-cofiniteness of $V$ implies $C_2$-cofiniteness of $V^G$. The proof bounds the length and height of monomials in strong generators representing classes in a relative $C_2$ quotient. The length bound follows from a good filtration and finite-group invariant theory. The height bound follows from differential equations for products of fields, together with identities for invariants and vacuum coefficients. The height bound also…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-29","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}