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Genus (Curve)

One of the Plücker Characteristics, defined by

p\equiv {\textstyle{1\over 2}}(n-1)(n-2)-(\delta+\kappa)={\textstyle{1\over 2}}(m-1)(m-2)-(\tau+\iota),

where $m$ is the class, $n$ the order, $\delta$ the number of nodes, $\kappa$ the number of Cusps, $\iota$ the number of stationary tangents (Inflection Points), and $\tau$ the number of Bitangents.

See also Riemann Curve Theorem


Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, p. 100, 1959.

© 1996-9 Eric W. Weisstein