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On effective non-vanishing and base-point-freeness

Yujiro Kawamata
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Abstract

Let $X$ be a complete normal variety, $B$ an effective $\mathbb{R}$-divisor on $X$, and $D$ a Cartier divisor on $X$. Assume that the pair $(X, B)$ is log terminal. We consider the problem whether $H^0(X, D) \ne 0$ and obtain some results in lower dimensions.

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Yujiro Kawamata. 2000-04-14. On effective non-vanishing and base-point-freeness. https://arxiv.org/abs/math/0003169

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