In the special case of curves this says that a divisor is ample if and only if it has positive degree, and for a smooth projective algebraic surface " S ", the Nakai Moishezon criterion states that " D " is ample if and only if its self-intersection number " D " . " D " is strictly positive, and for any irreducible curve " C " on " S " we have " D " . " C " > 0.
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