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 curve genus. This can be stated equivalently as the genus of a curve is unaltered by a birational transformation.

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

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Riemann Curve Theorem

Cite this as:

Weisstein, Eric W. "Riemann Curve Theorem." From MathWorld--A Wolfram Web Resource.

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