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

References

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