Twisted modules and co-invariants for commutative vertex algebras of jet schemes
OA Version
Citation
MM Szczesny. "Twisted modules and co-invariants for commutative vertex algebras of jet schemes."
Abstract
Let Zâđ¸k be an affine scheme over $\C$ and $\J Z$ its jet scheme. It is well-known that $\mathbb{C}[\J Z]$, the coordinate ring of $\J Z$, has the structure of a commutative vertex algebra. This paper develops the orbifold theory for $\mathbb{C}[\J Z]$. A finite-order linear automorphism g of Z acts by vertex algebra automorphisms on $\mathbb{C}[\J Z]$. We show that $\mathbb{C}[\J^g Z]$, where $\J^g Z$ is the scheme of g--twisted jets has the structure of a g-twisted $\mathbb{C}[\J Z]$ module. We consider spaces of orbifold coinvariants valued in the modules $\mathbb{C}[\J^g Z]$ on orbicurves [Y/G], with Y a smooth projective curve and G a finite group, and show that these are isomorphic to â[ZG].