Consider a fibration $f : S \to B$ of an algebraic surface $S$, (i.e. a $2$-dimensional, proper $k$-scheme) over a curve $B$ (i.e. $1$-dim ").
My question is quite banal, but till now I don't found a precise answer for it.
What is concretely the genus $g$ of a fibration in light of algebraic geometry?