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Masahiro Ohno

Classification of generalized polarized manifolds by their nef values

Keywords: Nef values, ample vector bundles, Fano bundles

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

Advances in Geometry, Walter de Gruyter

Print ISSN: 1615-715X
Volume: 6, 10/2006
Pages: 543 - 599

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