  For a discrete subgroup of an indefinite unitary group $U(1,n+1)$, $n\geq 1$,
consider the attached modular variety. Using local Borcherds products, we study
Heegner divisors in the local Picard group over a boundary component the
compactified variety. We obtain a criterion for local Heegner divisors to be
torsion elements in the local Picard group. As an application, we find that the
obstructions for a local Heegner divisor to be a torsion element can be
described through spaces of vector valued elliptic cusp forms spanned by
certain theta-series.
