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On the Nonemptiness of the Adjoint Linear System of Polarized Manifolds

Published online by Cambridge University Press:  20 November 2018

Yoshiaki Fukuma
Yoshiaki Fukuma*
Affiliation:
Department of Mathematics Faculty of Science Tokyo Institute of Technology Oh-okayama, Meguro-ku Tokyo 152 Japan, e-mail: fukuma@math.titech.ac.jp
*
Current address: Department of Mathematics College of Education Naruto University of Education Takashima, Naruto-cho, Naruto-shi 772-8502 Japan, e-mail: fukuma@naruto-u.ac.jp
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Abstract

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Let $(X,L)$ be a polarized manifold over the complex number field with dim$X=n$. In this paper, we consider a conjecture of M. C. Beltrametti and A. J. Sommese and we obtain that this conjecture is true if $n=3$ and ${{h}^{0}}\,(L)\,\ge \,2$, or $\dim\,\text{Bs}|L|\le 0$ for any $n\ge 3$. Moreover we can generalize the result of Sommese.

Keywords

14C2014J99Polarized manifoldadjoint bundle
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 3 , 01 September 1998 , pp. 267 - 278
Copyright
Copyright © Canadian Mathematical Society 1998

Footnotes

The author is a Research Fellow of the Japan Society for the Promotion of Science.

References

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