normal variety

An algebraic variety or an algebraic scheme XX is normal if at every point pp the stalk 𝒪 X,x\mathcal{O}_{X,x} is an integrally closed domain?. For every variety XX there is a morphism X→𝒳X\to \mathcal{X} which is universal among all morphisms from XX into normal varieties; 𝒳\mathcal{X} (or more precisely 𝒳\mathcal{X} together with the universal morphism) is said to be the normalization of XX.

Revised on March 6, 2013 19:24:34 by Zoran Å koda (