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Normal scheme
In
algebraic geometry
, an
algebraic variety
or scheme
X
is
normal
if it is normal at every point, meaning that the
local ring
at the point is an
integrally closed domain
. An
affine variety
X
(understood to be irreducible) is normal if and only if the ring
O
(
X
) of
regular functions
on
X
is an integrally closed domain. A variety
X
over a field is normal if and only if every
finite
birational morphism
from any variety
Y
to
X
is an isomorphism.
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