Nevanlinna invariant

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 $K_{X}+rD$ is in the closed real cone of effective divisors in the Néron–Severi group of X. It is expected that α(D) is always a rational number.

References

• Hindry, Marc; Silverman, Joseph H. (2000). Diophantine Geometry: An Introduction. Graduate Texts in Mathematics. Vol. 201. ISBN 0-387-98981-1. Zbl 0948.11023.