isNef D
A $\QQ$-Cartier divisor is nef (short for numerically effective or numerically eventually free) if the intersection product of the divisor with every complete irreducible curve is nonnegative. The definition depends only on the numerical equivalence class of the divisor. For a torus-invariant $\QQ$-Cartier divisor on a complete normal toric variety, the following are equivalent:
A torus-invariant Cartier divisor is nef if and only if it is basepoint free; in other words, the associated line bundle is generated by its global sections.
On a Hirzebruch surface, three of the four torus-invariant irreducible divisors are nef, and none are ample.
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Not every $\QQ$-Cartier nef divisor is basepoint free.
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There are smooth complete normal toric varieties with no nontrivial nef divisors.
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The most basic vanishing theorem for normal toric varieties states that the higher cohomology of coherent sheaf associated to a nef divisor is zero.
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