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On a question of Demailly-Peternell-Schneider

Abstract

This note aims to give an affirmative answer to an open question posed by Demailly-Peternell-Schneider [DPS] in 2001 and recently by Peternell [P] again. Let f:XYf:X\mapsto Y be a surjective morphism from a log canonical pair (X,D) onto a Q{\mathbb Q}-Gorenstein variety YY. If (KX+D)-(K_X+D) is nef, we show that KY-K_Y is pseudo-effective.Comment: J. Eur. Math. Soc. (to appear), minor corrections to some misleading misprint

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