Two ramified covers $\Rightarrow$ reducible ramification divisor? Let $X,X',X''$ be algebraic varieties and let $X''\to X'$ and $X'\to X$ be two ramified covers. Is the ramification divisor of the composition $X''\to X'\to X$ reducible?

Let $X=X'=X''=\Bbb{A}^1$ be the affine line, and let the two covers be $z \mapsto z^2$. Their composite is the (ramified) cover $z \mapsto z^4$, and the ramification divisor of this morphism is supported at $0$ only. This shows in particular that the ramification divisor can be irreducible.
