The Néron-Severi group of a complete normal variety 
over 
is the finitely generated quotient
group 
,
where 
is the group of Cartier divisors and 
is its subgroup of divisors algebraically equivalent
to zero. The subgroup 
consists of divisors numerically equal to zero.
For a smooth projective variety the equivalent line-bundle description is
 |
Here 
is the subgroup of line bundles algebraically equivalent
to the trivial bundle. The rank of 
is the Picard number.
Over 
,
the real vector space 
agrees with the space of numerical divisor classes
used for the Picard number of a Fano
manifold.
