image of the canonical morphism of a spanned divisor

49 Views Asked by At

Take $S$ a complex algebraic projective surface and $M\in Div(S)$ a spanned divisor of $S$.
Due to the fact that $M$ is spanned we can define a morphism
$\phi_{[M]} :S \rightarrow \mathbb{P}^N$ with $N=h^0(M)-1$.
What can i say about the image of $S$ through $\phi_{[M]}$? is it a smooth curve?