Weber's theorem (Algebraic curves)

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 C′ having the same genus g > 1. If there is a rational correspondence φ between C and C′, then φ is a birational transformation.

References

• Coolidge, J. L. (1959). A Treatise on Algebraic Plane Curves. New York: Dover. p. 135. ISBN 0-486-60543-4. https://books.google.com/books?id=Y7WEf6V0XwgC&pg=PA135. 
• Weber, H. (1873). "Zur Theorie der Transformation algebraischer Functionen" (in German). Journal für die reine und angewandte Mathematik 76: 345–348. doi:10.1515/crll.1873.76.345. https://zenodo.org/record/2127807/files/article.pdf. 

Further reading

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

External links

• Weisstein, Eric W.. "Weber's Theorem". http://mathworld.wolfram.com/WebersTheorem.html.