Abstract
Let X, Y be Riemann surfaces and f: X → Y a non-constant holomorphic map. If a ∈ X, b = f(a) and w is a local coordinate at b with w(b) = 0, we set orda(f) = ord a(w o f). The integer b(a, f) = orda(f) − 1 is called the ramification index of f at a; f is a local homeomorphism at a if and only if b(a, f) = 0.
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© 1992 Springer Basel AG
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Narasimhan, R. (1992). Further Properties of Compact Riemann Surfaces. In: Compact Riemann Surfaces. Lectures in Mathematics ETH Zürich. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8617-8_11
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DOI: https://doi.org/10.1007/978-3-0348-8617-8_11
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-2742-2
Online ISBN: 978-3-0348-8617-8
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