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Remarks on quasi-polarized varieties
Published online by Cambridge University Press: 22 January 2016
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Let V be a variety, which means, an irreducible reduced projective scheme over an algebraically closed field of any characteristic. A line bundle L on V is said to be nef if LC ≧ 0 for any curve C in V. Thus, “nef” is never an abbreviation of “numerically equivalent to an effective divisor”. L is said to be big if k(L) = n = dim V. In case L is nef, it is big if and only if Ln > 0 (cf. [F7; (6.5)]. When L is nef and big, the pair (V, L) will be called a quasi-polarized variety.
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