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Zeuthen's Theorem

If there is a $(\nu,\nu')$ correspondence between two curves of Genus $p$ and $p'$ and the number of Branch Points properly counted are $\beta$ and $\beta'$, then

\begin{displaymath}
\beta+2\nu'(p-1)=\beta'+2\nu(p'-1).
\end{displaymath}

See also Chasles-Cayley-Brill Formula


References

Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, p. 246, 1959.




© 1996-9 Eric W. Weisstein
1999-05-26