Let $X$ be a smooth curve over $\mathbb C$. An $U(1)-$principal bundle over $X$ is a flat unitary line bundle. What is the exact definition of the latter? Is it a line bundle over $X$ with a hermitian form?
Thanks
Let $X$ be a smooth curve over $\mathbb C$. An $U(1)-$principal bundle over $X$ is a flat unitary line bundle. What is the exact definition of the latter? Is it a line bundle over $X$ with a hermitian form?
Thanks
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