Numerically effective

In algebraic geometry, a line bundle on a complete algebraic variety over a field is said to be nef if the degree of its restriction to every algebraic curve in the variety is non-negative. The term "nef" was introduced by Miles Reid as a replacement for the older terms "arithmetically effective" (Zariski 1962, definition 7.6) and "numerically effective", as well as for the phrase "numerically eventually free". (A line bundle is called semi-ample or "eventually free" if some positive power is basepoint-free.) The older terminology was confusing because nef divisors are not the same as divisors numerically equivalent to effective divisors. For example, a curve with negative self-intersection number on a surface is effective but not nef.

Every semi-ample divisor is nef, but not every nef divisor is numerically equivalent to a semi-ample divisor, or even to an effective divisor. For example, Mumford constructed a line bundle L on a suitable ruled surface X such that L has positive degree on all curves, but the intersection number c₁(L)² is zero. It follows that L is nef, but no positive multiple of the first Chern class c₁(L) is numerically equivalent to an effective divisor. (The first Chern class is an isomorphism from the Picard group of line bundles on a variety X to the group of Cartier divisors modulo linear equivalence.)

A Cartier divisor D on an algebraic variety X is said to be nef if the corresponding line bundle O(D) is nef on X. Equivalently, D is nef if

for any algebraic curve C in X, in the sense of intersection theory.

To work with inequalities, it is convenient to consider R-divisors, meaning finite linear combinations of Cartier divisors with real coefficients. The R-divisors modulo numerical equivalence form a real vector space N¹(X) of finite dimension, the Néron–Severi group tensored with the real numbers. The nef R-divisors form a closed convex cone in this vector space, called the nef cone. The interior of this cone is called the ample cone. For any projective variety X, Kleiman showed that a divisor is ample if and only if its numerical equivalence class lies in the interior of the nef cone. In particular, every ample line bundle is nef.

...
Wikipedia