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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 ...

Context: This question arose as I was reading the proof of Application 6.1 in Mumford's Abelian Varieties. However, I have extracted all of the relevant information below so this question should ...

EDIT: Let me try to make the question clearer. Consider the invertible sheaves $\mathcal{O}(d)$ over the projective space $\mathbb{P}^n$ where $d\in \mathbb{Z}$. Now, if $d>0$, among many ...