A line bundle is nef when its degree on every integral complete curve is nonnegative. Equivalently a Cartier divisor is nef when for every such curve. On a projective scheme, adding a positive ample class to a nef class makes it ample; taking limits in the intersection product shows that a nef divisor has nonnegative top self-intersection number.
For a nef divisor on an integral projective variety of dimension ,Indeed, combine asymptotic Riemann–Roch with cohomology growth for nef twists. Thus its normalized section-growth limit is , and it is big exactly when .
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