A ramification point of a nonconstant holomorphic map 
between Riemann surfaces is a point 
at which, in suitable coordinate
charts centered at 
and 
, the map has the form 
with 
. The integer 
is the ramification index
at 
,
and 
is a branch point.
Ramification Point
See also
Branch Point, Branched Covering Map, Ramification, Ramification IndexExplore with Wolfram|Alpha
References
Miranda, R. Algebraic Curves and Riemann Surfaces. Providence, RI: Amer. Math. Soc., 1995.Cite this as:
Weisstein, Eric W. "Ramification Point." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RamificationPoint.html