Geodesic
Picard groups for line bundles with connections
Journal of Singularities, Tome 18 (2018), pp. 215-237

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We study analogues of the usual Picard group for complex manifolds or non-singular complex algebraic varieties but instead of line bundles we study line bundles with connections. We choose an approach which works for both cases. We identify obstructions for the existence of a connection, or a connection which is even integrable or regular (integrable), and point out where one should be careful when passing from the analytic to the algebraic case.
DOI : 10.5427/jsing.2018.18j
Classification : 14C22, 53C05, 14C30, 55N30, 55N05 
@article{10_5427_jsing_2018_18j,
     author = {Helmut Hamm and L\^e D\~{u}ng Tr\'ang},
     title = {Picard groups for line bundles with connections},
     journal = {Journal of Singularities},
     pages = {215--237},
     publisher = {mathdoc},
     volume = {18},
     year = {2018},
     doi = {10.5427/jsing.2018.18j},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2018.18j/}
}
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Helmut Hamm; Lê Dũng Tráng. Picard groups for line bundles with connections. Journal of Singularities, Tome 18 (2018), pp. 215-237. doi: 10.5427/jsing.2018.18j

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