I am trying to understand concepts of Gerbes and their differential geometry as generalisation of line bundles and their differential geometry using Hitchin’s notes.
I am familiar with concepts of connections, curvature for principal bundles. I did not read separately for vector bundles/line bundles in particular.
There are some results about line bundles mentioned in article which I am not very comfortable with. For example, it says
The holonomy of a flat connection on a unitary line bundle is given by parallel translation around closed loops.
For a line bundle, when the holonomy is trivial we get a covariant constant trivialization of the bundle.
I am guessing it might be a better idea to actually read about connections/curvature/holonomy of line bundles in particular. I just need some rough idea.
Any reference is most welcome.