Remarks on quasi-polarized varieties

Abstract

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 L n > 0 (cf. [F7; (6.5)]. When L is nef and big, the pair ( V, L ) will be called a quasi-polarized variety .