Riemann Curve Theorem

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

References

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

• Heegaard Splitting
• Heegner Number
• Heesch Number
• Heesch's Problem
• Height
• Heilbronn Triangle Problem
• Heine-Borel Theorem
• Heine Hypergeometric Series
• Heisenberg Group
• Heisenberg Space
• Held Group
• Helen of Geometers
• Helicoid
• Helix
• Helly Number
• Helly's Theorem
• Helmholtz Differential Equation
• Helmholtz Differential Equation--Bipolar Coordinates
• Helmholtz Differential Equation--Cartesian Coordinates
• Helmholtz Differential Equation--Circular Cylindrical Coordinates
• Helmholtz Differential Equation--Confocal Ellipsoidal Coordinates
• Helmholtz Differential Equation--Confocal Paraboloidal Coordinates
• Helmholtz Differential Equation--Conical Coordinates
• Helmholtz Differential Equation--Elliptic Cylindrical Coordinates
• Helmholtz Differential Equation--Oblate Spheroidal Coordinates