On effective non-vanishing and base-point-freeness

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.

13 pages, Theorem 5.2 (3) is deleted