  We introduce and study the problem of finding necessary and sufficient
conditions under which a conformal blocks divisor on $\bar{M}_{0,n}$ is
nonzero. We give necessary conditions in type A, which are sufficient when
theta and critical levels coincide. We show that divisors are subject to
additive identities, dependent on ranks of the underlying bundle. These
identities amplify vanishing and nonvanishing results and have other
applications.
