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aglearner
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A basic question on the definition of Cartan-Remmert reduction and holomorphic convexity

Here is a definition of holomorphic convexity taken from the notes of Eyssidieux:

Defintion. A complex analytic space $S$ is holomorphically convex if there is a proper holomorphic morphism $\pi: S\to T$ with $\pi_*O_S=O_T$ such that $T$ is a Stein space. $T$ is then called Cartan-Remmert reduction of $S$.

Questions. 1) Is this correct that Cartan-Remmert reduction is unique is if exists?

  1. Do I understand correctly, that $\pi_*O_S=O_T$ just means that $\pi$ is a surjective map and all its fibers are connected?
aglearner
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