ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

4. Algebraic Geometry

1991 MS Classification: 14J40, 14E30, 14J10, 14J60 Ohno, Masahiro, Waseda University, Japan On nef values of determinants of ample vector bundles. Let M be an n-dimensional projective manifold over the complex number field and E an ample vector bundle on M. The nefness of the adjoint bundle K_{M} + det E has been studied by several authors for r ≥ n − 2. In this talk, we study the nef value τ of the polarized manifold (M, det E) for r ≤ n + 1. We show that τ ≤ (n + 1)/r if r ≤ n + 1, and classify the pair (M, E) in the following cases: (1) τ = (n + 1)/r and r ≤ n + 1, (2) n/r ≤ τ and r ≤ n, (3) (n − 1)/r < τ < n/r and r ≤ n − 1. These results genelarize the theorems concerning the nefness of the adjoint bundles previously obtained by Y. -G. Ye and Q. Zhang, T. Fujita, and T. Peternell.