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Relative adjoint transcendental classes and Albanese map of compact Kähler manifolds with nef Ricci curvature. (English) Zbl 1392.32010
Oguiso, Keiji (ed.) et al., Higher dimensional algebraic geometry. In honour of Professor Yujiro Kawamata’s sixtieth birthday. Proceedings of the conference, Tokyo, Japan, January 7–11, 2013. Tokyo: Mathematical Society of Japan (MSJ) (ISBN 978-4-86497-046-4/hbk). Advanced Studies in Pure Mathematics 74, 335-356 (2017).
Summary: We establish here the surjectivity of the Albanese map corresponding to compact Kähler manifold whose anti-canonical bundle is nef. This answers a question raised by J.-P. Demailly et al. [J. Algebr. Geom. 3, No. 2, 295–345 (1994; Zbl 0827.14027)]. One of the main techniques we are using is the positivity of the relative canonical bundle associated to Kähler fiber spaces, obtained via the “psh variation” of fiber-wise twisted Kähler-Einstein metrics.
For the entire collection see [Zbl 1388.14012].

32Q15 Kähler manifolds
32Q20 Kähler-Einstein manifolds