Branch index
From Encyclopedia of Mathematics - Reading time: 1 min
The sum $ V= \sum (k - 1) $
of the orders of the branch points (cf. Branch point) of a compact Riemann surface $ S $,
regarded as an $ n $-
sheeted covering surface over the Riemann sphere, extended over all finite and infinitely-distant branch points of $ S $.
The branch index is connected with the genus $ g $
and number of sheets $ n $
of $ S $
by:
$$ V = 2 (n + g - 1). $$
See also Riemann surface.
References[edit]
| [1] | G. Springer, "Introduction to Riemann surfaces" , Addison-Wesley (1957) pp. Chapt.10 MR0092855 Zbl 0078.06602 |
Comments[edit]
References[edit]
| [a1] | D. Mumford, "Algebraic geometry" , 1. Complex projective varieties , Springer (1976) MR0453732 Zbl 0356.14002 |
How to Cite This Entry: Branch index (Encyclopedia of Mathematics) | Licensed under CC BY-SA 3.0. Source: https://encyclopediaofmath.org/wiki/Branch_index12 views | ↧ Download this article as ZWI file
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