Riemann-Roch theorem

From Citizendium
Revision as of 01:12, 16 February 2007 by imported>David Lehavi (typo correction)
Jump to navigation Jump to search

In algebraic geometry the Riemann-Roch theorem states that if is a smooth algebraic curve, and is an invertible sheaf on then the the following properties hold:

  • The Euler characteristic of is given by
  • There is a canonical isomorphism

Generalizations

Proofs

Using modern tools, the theorem is an immediate consequence of Serre's duality.