Weber's theorem (Algebraic curves) explained

In mathematics, Weber's theorem, named after Heinrich Martin Weber, is a result on algebraic curves. It states the following.

Consider two non-singular curves C and having the same genus g > 1. If there is a rational correspondence φ between C and , then φ is a birational transformation.

References

• Book: Coolidge, J. L. . A Treatise on Algebraic Plane Curves . New York . Dover . 135 . 1959 . 0-486-60543-4 .
• H.. Weber. Heinrich Martin Weber. Journal für die reine und angewandte Mathematik. 76. 1873. 345–348. Zur Theorie der Transformation algebraischer Functionen. German. 10.1515/crll.1873.76.345.

Further reading

• 10.4099/jjm1924.18.0_759 . Theory of conformal mapping of a multiply connected domain . 1941 . Tsuji . Masatsugu . Japanese Journal of Mathematics :Transactions and Abstracts . 18 . 759–775. free .