  This paper is a sequel to math.AG/9803041. It consists of three parts. In the
first part we give certain construction of vertex algebras which includes in
particular the ones appearing in op. cit.
  In the second part we show how the cohomology ring $H^*(X)$ of a smooth
complex variety $X$ could be restored from the correlation functions of the
vertex algebra $R\Gamma(X;\Omega^{ch}_X)$.
  In the third part, we prove first a useful general statement that the sheaf
of loop algebras over the tangent sheaf $\Cal{T}_X$ acts naturally on
$\Omega^{ch}_X$ for every smooth $X$ (see \S 1). The Z-graded vertex algebra
$H^*(X;\Omega^{ch}_X)$ seems to be a quite interesting object (especially for
compact $X$). In \S 2, we compute $H^0(CP^N;\Omega^{ch}_{CP^N})$ as a module
over $\hat{sl}(N+1)$.
