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The local Picard group at a generic point of the one-dimensional Baily-Borel boundary of
a Hermitean symmetric quotient of type 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...
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