$C_2$-cofiniteness of finite-group orbifolds
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…
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