Branch index

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

[1]	G. Springer, "Introduction to Riemann surfaces" , Addison-Wesley (1957) pp. Chapt.10 MR0092855 Zbl 0078.06602

References

[a1]	D. Mumford, "Algebraic geometry" , 1. Complex projective varieties , Springer (1976) MR0453732 Zbl 0356.14002