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Branch index

From Encyclopedia of Mathematics
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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
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article