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Birkhoff decomposition vanishing of the Chern numbers of the holomorphic line bundles of the Birkhoff-Grothendieck decomposition, is some statement I read off in One of Connes papers. Without going ...

Let $L$ be a line bundle over a compex manifold $X$, a square-root of $L$ is a line bundle $M$ such that $M^{\otimes2}=L$. My question is when the square-root of Line Bundle is unique?

This is a somewhat speculative question, so bear with that (or not, as is your preference). Let $X$ be a smooth projective variety, and let $\omega_X$ be its canonical sheaf. The Euler class of ...