A question about line bundle

Let M be a compact complex projective manifold, i.e., we can embedded M into \mathbb{P} ^N for some N.

Assume L be a line bundle on \mathbb{P} ^N, and \pi^{-1}(L) be corresponding line bundle on M. Now, we have if  s is a holomorphic section on L, it is also a holomorphic section on \pi^{-1}(L). How about a holomorphic section on \pi^{-1}(L)? Can we say anything on L?

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