A nef line bundle on a projective variety is a line bundle with nonnegative
degree on every irreducible curve. Its numerical class lies in the closure of the
ample cone. For a holomorphic line bundle on a compact
complex manifold, analytic nefness means that
for each 
a smooth Hermitian metric exists with curvature
bounded below by 
,
for a fixed Hermitian form 
.
The projective definitions agree. A smooth semipositive metric implies nefness, but the definition of nefness permits a different metric for each 
. Nefness of the tautological quotient line
bundle defines a nef vector bundle.
