Citizendium - a community developing a quality comprehensive compendium of knowledge, online and free. Click here to join and contribute—free |

Many thanks . June 2014 donors; special to Darren Duncan. July 2014 donations open; need minimum total $100. Let's exceed that. Donate hereDonating gifts yourself and CZ. -- June 2014 Election Results -- |

# Genus-degree formula

### From Citizendium, the Citizens' Compendium

(Redirected from Genus degree formula)

In classical algebraic geometry, the genus-degree formula relates the degree of a non-singular plane curve with its arithmetic genus via the formula:

A singularity of order *r* decreases the genus by .^{[1]}

### Proofs

The proof follows immediately from the adjunction formula. For a classical proof see the book of Arbarello, Cornalba, Griffiths and Harris.

### References

- ↑ Semple and Roth,
*Introduction to Algebraic Geometry*, Oxford University Press (repr.1985) ISBN 0-19-85336-2. Pp.53-54

- Arbarello, Cornalba, Griffiths, Harris. Geometry of algebraic curves. vol 1 Springer, ISBN 0387909974, appendix A.
- Grffiths and Harris, Principles of algebraic geometry, Wiley, ISBN 0-471-05059-8, chapter 2, section 1