  We consider two complexes. The first complex is the twisted de Rham complex
of scalar meromorphic differential forms on projective line, holomorphic on the
complement to a finite set of points. The second complex is the chain complex
of the Lie algebra of $\mathfrak{sl}_2$-valued algebraic functions on the same
complement, with coefficients in a tensor product of contragradient Verma
modules over the affine Lie algebra $\hat{{\mathfrak{sl}_2}}$. In [Schechtman
V., Varchenko A., Mosc. Math. J. 17 (2017), 787-802] a construction of a
monomorphism of the first complex to the second was suggested and it was
indicated that under this monomorphism the existence of singular vectors in the
Verma modules (the Malikov-Feigin-Fuchs singular vectors) is reflected in the
relations between the cohomology classes of the de Rham complex. In this paper
we prove these results.
