Let $f \colon X \longrightarrow Y$ be a finite morphism of degree $n \geq 2$ between smooth compact, complex surfaces.
Let $B \subset Y$ be the branch divisor of $f$ and assume that the corresponding branching order is $2$, namely $$f^*B = 2R + R_0,$$ where $R \subset X$ is the ramification divisor and $R_0$ is the residual curve (sometimes this condition is expressed by saying that $f$ is a generic cover).
Question. If the branch locus $B$ is a smooth divisor, is it true that $RR_0=0$?
I know that the answer is yes for $n=2$ (trivially, because $R_0$ is empty in that case) and for $n=3$ (as a consequence of the general theory of triple covers developed by R. Miranda), but what happens for general $n$?
