Branch index
From Encyclopedia of Mathematics
The sum 
of the orders of the branch points (cf. Branch point) of a compact Riemann surface 
, regarded as an 
-sheeted covering surface over the Riemann sphere, extended over all finite and infinitely-distant branch points of 
. The branch index is connected with the genus 
and number of sheets 
of 
by:
 |
See also Riemann surface.
References
| [1] | G. Springer, "Introduction to Riemann surfaces" , Addison-Wesley (1957) pp. Chapt.10 MR0092855 Zbl 0078.06602 |
Comments
References
| [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. URL: http://encyclopediaofmath.org/index.php?title=Branch_index&oldid=46147
Branch index. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Branch_index&oldid=46147
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article