(This is a very naïve question.)
Work over $\mathbb{C}$. We say a smooth algebraic surface $S$ is a section if there is a smooth projective $3$-fold $X$ and $0 \neq F \in H^{0}(X,-K_{X})$, with $S = \{F=0\} \subset X$.
Is this class of algebraic surfaces classified? Are there some easy restrictions on $S$?