Picard groups for line bundles with connections

Journal of Singularities
volume 18 (2018), 215-237

Received: 30 December 2017. Accepted: 17 May 2018.

DOI: 10.5427/jsing.2018.18j

Add a reference to this article to your citeulike library.

Abstract:

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.

Keywords:

Picard group, connection, Deligne cohomology, Atiyah class

Mathematical Subject Classification:

14C22, 53C05, 14C30, 55N30, 55N05

Author(s) information: