Geodesic
On the Local Picard Group
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Singularities and applications, Tome 267 (2009), pp. 138-145

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In his book SGA 2, A. Grothendieck developed Lefschetz theorems for the Picard group, the aim being to compare the Picard group of a projective variety with the one of a hyperplane section. An intermediate object is the Picard group of the formal completion along the hyperplane section. Here we proceed similarly but in the local complex analytic context. The use of the exponential sequence leads to analytic as well as topological depth conditions. 
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     author = {H. A. Hamm},
     title = {On the {Local} {Picard} {Group}},
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H. A. Hamm. On the Local Picard Group. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Singularities and applications, Tome 267 (2009), pp. 138-145. http://geodesic.mathdoc.fr/item/TM_2009_267_a10/