  We generalize to the case of singular blocks the result in \cite{BeLa} that
describes the center of the principal block of a small quantum group in terms
of sheaf cohomology over the Springer resolution. Then using the method
developed in \cite{LQ1}, we present a linear algebro-geometric approach to
compute the dimensions of the singular blocks and of the entire center of the
small quantum group associated with a complex semisimple Lie algebra. A
conjectural formula for the dimension of the center of the small quantum group
at an $l$th root of unity is formulated in type A.
