Classification of generalized polarized manifolds by their nef values

Details Classification of generalized polarized manifolds by their nef values Classification of generalized polarized manifolds by their nef values

2005-03-07

arxiv.org/abs/math/0503119v1

Mathematics

Algebraic Geometry

53 pages

Scientific paper

Let (M,E) be a generalized polarized manifold, i.e., a pair of an n-dimensional smooth projective variety and an ample vector bundle E of rank r on M. Let t be the nef value of a polarized manifold (M, det E), i.e., the minimum of the set of real numbers s such that K+s det E is nef; we have tr<= n+1 by Mori's theory. In this paper we classify the pairs (M,E) in the following two cases: (1) n-2<= tr and t >= 1; (2) n+1-tr< t <= 1.

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