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On the Nonemptiness of the Adjoint Linear System of Polarized Manifolds
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- Journal:
- Canadian Mathematical Bulletin / Volume 41 / Issue 3 / 01 September 1998
- Published online by Cambridge University Press:
- 20 November 2018, pp. 267-278
- Print publication:
- 01 September 1998
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- Article
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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.
