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

References

  • {{cite book | author=Coolidge, J. L. | title=A Treatise on Algebraic Plane Curves | location=New York | publisher=Dover | page=135 | year=1959 | isbn=0-486-60543-4 | url = https://books.google.com/books?id=Y7WEf6V0XwgC&pg=PA135 }}
  • {{cite journal|first=H.|last=Weber|authorlink=Heinrich Martin Weber|journal=Journal für die reine und angewandte Mathematik|volume=76|year=1873|pages=345–348|url=https://zenodo.org/record/2127807|language=German|title=Zur Theorie der Transformation algebraischer Functionen|doi=10.1515/crll.1873.76.345}}

Further reading

  • {{cite journal |doi=10.4099/jjm1924.18.0_759 |title=Theory of conformal mapping of a multiply connected domain |year=1941 |last1=Tsuji |first1=Masatsugu |journal=Japanese Journal of Mathematics :Transactions and Abstracts |volume=18 |pages=759–775|doi-access=free }}