The local Picard group at a generic point of the one-dimensional Baily-Borel boundary of a Hermitean symmetric quotient of type O ( 2 , n ) is computed. The main ingredient is a local version of Borcherds’ automorphic products. The local obstructions for a Heegner divisor to be principal are given by certain theta series with harmonic coefficients. Sometimes they generate Borcherds’ space of global obstructions. In these particular cases we obtain a simple proof of a result due to the first author: Suppose that Γ ⊂ O ( 2 , n ) is the orthogonal group attached to an even unimodular lattice. Then every meromorphic modular form for Γ , whose zeros and poles lie on Heegner divisors, is given by a Borcherds product.