Classification of generalized polarized manifolds by their nef values

2005/03/07 by Masahiro Ohno, Ohno, Masahiro
Mathematics · #14E30 (Secondary) #14J60 #14N30 (Primary) 14J45 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG #msc:14E30 #msc:14J45 #msc:14J60 #msc:14N30

paper · pdf · doi:10.48550/arxiv.math/0503119

53 pages

arxiv created 2005/03/07 · openalex publication_date 2005/03/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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