A normal variety is an algebraic variety whose local rings are integrally
closed integral domains. Thus each local
ring contains every element of its field
of fractions that is integral over that local ring
(Hartshorne 1977). Normality does not imply smoothness. Every smooth
variety is normal, while the complex quadric 
in 
is a normal surface with a singularity
at the origin.
On a normal variety, integral subvarieties of codimension one define Weil divisors. The canonical divisor and log canonical pair definitions use this setting.
