  We introduce logarithmic Picard algebroids, a natural class of Lie algebroids
adapted to a simple normal crossings divisor on a smooth projective variety. We
show that such algebroids are classified by a subspace of the de Rham
cohomology of the divisor complement determined by its mixed Hodge structure.
We then solve the prequantization problem, showing that under the appropriate
integrality condition, a log Picard algebroid is the Lie algebroid of
symmetries of what is called a meromorphic line bundle, a generalization of the
usual notion of line bundle in which the fibres degenerate along the divisor.
We give a geometric description of such bundles and establish a classification
theorem for them, showing that they correspond to a subgroup of the holomorphic
line bundles on the divisor complement. Importantly, these holomorphic line
bundles need not be algebraic. Finally, we provide concrete methods for
explicitly constructing examples of meromorphic line bundles, such as for a
smooth cubic divisor in the projective plane.
