Geodesic
The Albanese map for manifolds without meromorphic functions
Matematičeskie zametki, Tome 20 (1976) no. 2, pp. 207-214.

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In this paper, the investigation of compact complex manifolds on which there are no nonconstant meromorphic functions, begun in [1], is continued. Here, in the case when such a manifold is kähler, it is proved that the kodaira dimension of the general fiber of the Albanese map $\leqslant0$; the case when the irregularity is equal to the dimension minus one is studied in more detail. 
@article{MZM_1976_20_2_a5,
     author = {V. A. Krasnov},
     title = {The {Albanese} map for manifolds without meromorphic functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {207--214},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_2_a5/}
}
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V. A. Krasnov. The Albanese map for manifolds without meromorphic functions. Matematičeskie zametki, Tome 20 (1976) no. 2, pp. 207-214. http://geodesic.mathdoc.fr/item/MZM_1976_20_2_a5/