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.
