Numerically effective

Numerically effective

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

:Dcdot C ge 0

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

References

*Sommese, A. J., [http://eom.springer.de/A/a110410.htm "Adjunction theory"] , in [http://eom.springer.de/default.htm "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.


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