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Genus-degree formula
From Citizendium, the Citizens' Compendium
In classical algebraic geometry, the genus-degree formula relates the degree d of a plane curve 
with its arithmetic genus g via the forumla:
g = (d − 1)(d − 2)
Proofs
The proof is immediate by adjunction. For a classical proof see the first reference below.
References
- Arbarello, Cornalba, Griffiths, Harris. Geometry of algebraic curves. vol 1 Springer, ISBN 0387909974, appendix A.
- Grffiths and Harris, Principls of algebraic geometry, Wiley, ISBN 0-471-05059-8, chapter 2, section 1
