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Remarks on quasi-polarized varieties

Published online by Cambridge University Press:  22 January 2016

Takao Fujita
Takao Fujita*
Affiliation:
Department of Mathematics, College of Arts and Sciences University of Tokyo, Komaba, Meguro, Tokyo 153, Japan
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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.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 115 , September 1989 , pp. 105 - 123
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1989

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