Varieties fibred over abelian varieties with fibres of log general type

doi:10.1016/j.aim.2014.10.023

Advances in Mathematics

Volume 270, 22 January 2015, Pages 206-222

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Abstract

Let $(X, B)$ be a complex projective klt pair, and let $f : X \to Z$ be a surjective morphism onto a normal projective variety with maximal albanese dimension such that $K_{X} + B$ is relatively big over Z. We show that such pairs have good log minimal models.

MSC

14E30

11J95

Keywords

Minimal model conjecture

Abundance conjecture

Iitaka conjecture

Abelian varieties

Fourier–Mukai transform