The Picard number 
of a smooth projective variety is the rank
of its Néron-Severi group. Equivalently
over 
,
it is the dimension of 
, the real space of divisors modulo numerical equivalence.
Numerical equivalence identifies divisors having the same intersection degree with
every curve. For projective space of positive
dimension the Picard number is 1.
A product of 
positive-dimensional projective spaces has Picard number 
. These products give the equality examples in the generalized
Mukai conjecture when their factor dimensions are
equal.
