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Classification of generalized polarized manifolds by their nef values
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Masahiro Ohno
Published/Copyright:
October 16, 2006
Abstract
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 τ be the nef value of a polarized manifold (M, det ℰ), i.e., the minimum of the set of real numbers t such that KM + t det ℰ is nef; we have τr ≤ n + 1 by Mori's theory. In this paper we classify the pairs (M, ℰ) in the following two cases: (1) n − 2 ≤ τr and τ ≥ 1; (2) n + 1 − τr < τ ≤ 1.
Received: 2005-03-04
Revised: 2005-08-12
Published Online: 2006-10-16
Published in Print: 2006-10-01
© Walter de Gruyter
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Articles in the same Issue
- On the critical points of a Riemannian surface
- The extrinsic polyharmonic map heat flow in the critical dimension
- Shult sets and translation ovoids of the Hermitian surface
- Classification of generalized polarized manifolds by their nef values
- Fano manifolds of coindex four as ample sections
- Groups generated by affine perspectivities
- Definability results for the Poisson equation
- Jung's theorem for a pair of Minkowski spaces
Articles in the same Issue
- On the critical points of a Riemannian surface
- The extrinsic polyharmonic map heat flow in the critical dimension
- Shult sets and translation ovoids of the Hermitian surface
- Classification of generalized polarized manifolds by their nef values
- Fano manifolds of coindex four as ample sections
- Groups generated by affine perspectivities
- Definability results for the Poisson equation
- Jung's theorem for a pair of Minkowski spaces
