Let $M$ be a complex manifold admitting an atlas with each chart biholomorphic to $\mathbb{C}^n$ and transition maps being rational functions. 

Is it true that there exists a smooth integral separated scheme $X$ of finite type over $\mathbb{C}$ such that its set of complex points $X(\mathbb{C})$ endowed with analytic topology is biholomorphic to $M$? Is the converse true (i.e. if such a scheme exists, then there has to exist an atlas as in the first sentence)?