# Schlicht domain

What is a schlicht domain over $\mathbb{C}^n$? How is it different from a domain in $\mathbb{C}^n$? Examples?

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Schlicht domain over ${\mathbb C}^n$ is the same as a domain in ${\mathbb C}^n$. The point is that one also defines domains over ${\mathbb C}^n$ as connected complex manifolds $M^n$ equipped with a locally biholomorphic map $f:M^n\to {\mathbb C}^n$. The schlicht property just means that $f$ is 1-1.
So, every domain in $\mathbb C^n$ is schlicht. – Saurabh T Nov 22 '12 at 22:50