Geodesic
$n$-Dimensional compact complex analytic manifolds having $n-1$ algebraically independent meromorphic functions
Matematičeskie zametki, Tome 10 (1971) no. 2, pp. 145-149

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Manifolds of the type indicated in the title have been investigated for $n=2$ by Kodaira, whose methods were adopted by Kawai in application to the case $n=3$. In the present note we use the same methods to investigate the general case. We deduce a bimeromorphic classification of the manifolds in question. Their complete description can be obtained on the basis of certain results of Hironaka. 
@article{MZM_1971_10_2_a3,
     author = {Zh. Goligo},
     title = {$n${-Dimensional} compact complex analytic manifolds having $n-1$ algebraically independent meromorphic functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {145--149},
     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_10_2_a3/}
}
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Zh. Goligo. $n$-Dimensional compact complex analytic manifolds having $n-1$ algebraically independent meromorphic functions. Matematičeskie zametki, Tome 10 (1971) no. 2, pp. 145-149. http://geodesic.mathdoc.fr/item/MZM_1971_10_2_a3/