info prev up next book cdrom email home

Riemann Curve Theorem

If two algebraic plane curves with only ordinary singular points and Cusps are related such that the coordinates of a point on either are Rational Functions of a corresponding point on the other, then the curves have the same Genus (Curve). This can be stated equivalently as the Genus of a curve is unaltered by a Birational Transformation.


Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, p. 120, 1959.

© 1996-9 Eric W. Weisstein