Understanding Ramification Points - Mathematics Stack Exchange I really don't understand how to calculate ramification points for a general map between Riemann Surfaces If anyone has a good explanation of this, would they be prepared to share it? Disclaimer:
Branched cover in algebraic geometry - Mathematics Stack Exchange Many of these references eventually mention "branch" or "ramification" in passing or loosely, as if assuming the reader knows about it So my questions are: What are the definitions of "branched covering" and "ramification"? What is the map $\pi$ explicitly? Is there a code of ethics among algebraic geometers to make simple things harder for
what does it mean for a prime at infinity to ramify? The above definition of ramification for real places is the usual one, justified e g by the ramification index 2 which appears in a complex valuation over a real one (see Joequinn's answer) However the same phenomenon could also be interpreted as the splitting of the real place under the complex one
How we can know the ramification ideals geometrically? How to actually compute the ramification index and inertia degree in practice is a whole other matter—my answer is just meant to give the abstract connection to geometry and some intuition about how it relates to the classical notion of ramification