Let $X$ be a complex algebraic surface. Let $D$ be a divisor. Assume that $D$ is base point free. Then the linear system $|D|$ defines a morphism $$\varphi:X\to \mathbb{P}^N.$$
I wonder if the following is true.
$\varphi$ is generically finite if and only if $D^2>0$.
The question comes when I read Friedman's Algebraic Surfaces and Holomorphism Vector Bundles. After defining eventually base point free divisor (p.21), there is a paragraph and I am stuck on the sentence
... (3rd line) We assume that $\varphi_{nD}$ is generically finite, or equivalently that $D$ is big. ...
The definition of big divisor is that $D^2>0$.
