Ramification locus

In mathematics, a branched covering is a map that is almost a covering map, except on a small set.

In topology, a map is a branched covering if it is a covering map everywhere except for a nowhere-dense set known as the branch set. Examples include the map from a wedge of circles to a single circle, where the map is a homeomorphism on each circle.

In algebraic geometry, the term branched covering is used to describe morphisms ${\displaystyle f}$ from an algebraic variety ${\displaystyle V}$ to another one ${\displaystyle W}$, the two dimensions being the same, and the typical fibre of ${\displaystyle f}$ being of dimension 0.

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