Anti-canonical divisorial contractions of weak Fano $3$-folds

Question

Let $X$ be a smooth weak Fano but not Fano $3$-fold ($-K_X$ is nef and big but not ample). Then the anti-canonical morphism $\phi:X\rightarrow W$ (the morphsim induced by the linear system $|-mK_X|$ some $m\gg 0$) induces is a birational contraction.

Assume that $\phi$ contracts a divisor. Could such divisor be contracted to a point or must it be necessarily contracted to a curve?

Answer 1

What about taking the following example: consider $\mathbb P^1$ bundle over $\mathbb P^2$ given by the projectivisation of $\mathbb P(O\oplus O(-3))$ over $\mathbb P^2$. The linear system $-mK_X$ contracts $\mathbb P^2$ to a point.