In mathematics, the Nevanlinna invariant of an ample divisor D on a normal projective variety X is a real number connected with the rate of growth of the number of rational points on the variety with respect to the embedding defined by the divisor.
Formally, α(D) is the infimum of the rational numbers r such that
is in the closed real cone of effective divisors in the Néron–Severi group of X.
The Nevanlinna invariant has similar formal properties to the abscissa of convergence of the height zeta function and it is conjectured that they are essentially the same.
[1] Let X be a projective variety over a number field K with ample divisor D giving rise to an embedding and height function H, and let U denote a Xariski open subset of X.