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Degree-genus formula

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In mathematics, the degree-genus formula states that if $C\subset\mathbb{P}^2$ is a smooth algebraic curve of degree $d$ , then it has genus

$g=\frac{1}{2}(d-1)(d-2).$

If the algebraic curve $C$ is not smooth, then the genus will be less than the above number.

[edit] References

Kulikov, Viktor S. (2001), "Genus of a curve", in Hazewinkel, Michiel, Encyclopaedia of Mathematics, Kluwer Academic Publishers, ISBN 978-1556080104

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Retrieved from "http://en.wikipedia.org/wiki/Degree-genus_formula"

Categories: Geometry stubs | Algebraic curves

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