Weber's theorem

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.
  • Weber, H. (1873). "Zur Theorie der Transformation algebraischer Functionen". Journal für die reine und angewandte Mathematik (in German). 76: 345–348.


This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.