How to prove line bundle L is trivial if and only if its dual bundle us trivial ?
2026-03-28 03:27:36.1774668456
How to prove line bundle L is trivial if and only if its dual bundle us trivial?
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The double dual of $L$ is isomorphic to $L$. So since the dual of the trivial bundle is trivial, we are done.
My first thought was that in the Picard group, the dual of a line bundle is it's inverse, so if the inverse of $L$ is the identity, it is pretty clear that $L$ is the identity.