Surjective inverse-polynomial germ projection without even covering
= Surjective inverse-polynomial germ projection without even covering
The inverse germs of $w^3-3w$ over $\mathbb C$ form the connected surface $\mathbb C\setminus\{-1,1\}$. Its projection is surjective and locally biholomorphic, but the fibres have three points generically and one point at each critical value $\pm2$, so it is not an evenly covered topological covering.