Numerically effective

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A line bundle on an algebraic variety is said to be numerically effective (in short, nef ), if the degree of the restriction to any algebraic curve of the variety is non negative.

In particular, every ample line bundle is nef.

Similarly, a Cartier divisor D on an algebraic variety X is nef, if

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

[edit] References

• Sommese, A. J., "Adjunction theory", in Encyclopaedia of Mathematics, Michiel Hazewinkel (editor), Springer-Verlag (2002). ISBN 1-4020-0609-8.
• Lazarsfeld, R., Positivity in Algebraic Geometry I, Springer-Verlag (2004). ISBN 3-540-22533-1.