On factorization and vector bundles of conformal blocks from vertex algebras
Modules over conformal vertex algebras give rise to sheaves of coinvariants and conformal blocks on moduli of stable pointed curves. Here we prove the factorization conjecture for these sheaves. Our results apply in arbitrary genus and for a large class of vertex algebras. As an application, sheaves defined by finitely generated admissible modules over vertex algebras satisfying natural hypotheses are shown to be vector bundles. Factorization is essential to a recursive formulation of invariants, like ranks and Chern classes, and to produce new constructions of rational conformal field theories and cohomological field theories.