The Nkron-Sevcri group of a (nonsingular projective) varicty is, by
definition, the group of divisors rnodulo algebraic equivalence, which is
known to be a fiuitcly generated abelian group (cf. [2]). Its rank is called
the Picard number of the variety. Thus the Nkron-Severi group is defined
in purely algebro-geometric terms, but it is a rather delicate invariant of
arithmetic nature. Perhaps, because of this reason, it usually requires some
nontrivial work before one can determine the l'icard number of a given
variety, let alone the full structure of its N6ron-Severi group. This is the
case even for algebraic surfaces over the field of complex numbers, where
it can be regarded as the subgroup of the cohornology group I12(X, Z)
characterized by the LefscheLz criterion.