Twisted modules and co-invariants for commutative vertex algebras of jet schemes

Let Z subset of A(k) be an affine scheme over C and JZ its jet scheme. It is well-known that C[JZ], the coordinate ring of JZ, has the structure of a commutative vertex algebra. This paper develops the orbifold theory for C[JZ]. A finite-order linear automorphism g of Z acts by vertex algebra automorphisms on C[JZ]. We show that C[J(g)Z], where J(G)Z is the scheme of g-twisted jets has the structure of a g-twisted C[JZ] module. We consider spaces of orbifold coinvariants valued in the modules C[J(g)Z] on orbicurves [Y/G], with Y a smooth projective curve and G a finite group, and show that these are isomorphic to C[Z(G)]. (C) 2018 Elsevier Inc. All rights reserved.