Conformal blocks from vertex algebras and their connections on ℳg,n

We show that coinvariants of modules over vertex operator algebras give rise to quasi-coherent sheaves on moduli stable pointed curves. These generalize Verlinde bundles or vector conformal blocks defined using affine Lie studied first by Tsuchiya-Kanie, Tsuchiya-Ueno-Yamada, and extend work a number researchers. The carry twisted logarithmic D-module structure, hence support projectively flat connection. identify the Atiyah algebra acting them, generalizing Tsuchimoto for algebras.