Let $M^n$ and $N^n$ be two compact complex (or complex projective) manifolds. Let $f: M\to N$ be a holomorphic map of degree one. How to prove that for each $x\in N$ the set $f^{-1}(x)$ is simply-connected?
Topology of the preimage of a point for degree one holomorphic maps
Dmitri Panov
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