I am looking for a suitable reference to put in a bibliography for the following fact:


Let $f: X \rightarrow Y$ be a surjective morphism between normal projective varieties. Let $D$ be a $\mathbb{Q}$-divisor on $Y$. If $f^\*D$ is semi-ample, so is $D$.


It is part of the content of Lemma 3.6 in these notes:


<http://math.mit.edu/~mckernan/Teaching/07-08/Autumn/18.735/l_3.pdf>


I would just like to have a more formal reference to include in my bibliography, like a book or a paper.



Reference request: $f^*D$ semi-ample, then $D$ semi-ample
This is proved in (1.20) THEOREM of Fujita, T. Semipositive line bundles, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 30 (1983), 353–378.


You can download this paper from <https://repository.dl.itc.u-tokyo.ac.jp/index.php?action=repository_view_main_item_detail&item_id=39567&item_no=1&page_id=28&block_id=31>


