Abstract
We give an affirmative answer to an open question posed by Demailly-Peternell-Schneider in 2001 and recently by Peternell. Let $f:X\rw Y$ be a surjective morphism from a log canonical pair $(X,D)$ onto a $\bQ$-Gorenstein variety $Y$. If $-(K\_X+D)$ is nef, we show that $-K\_Y$ is pseudo-effective.
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