Abstract
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 kahler, it is proved that the kodaira dimension of the general fiber of the Albanese map s⩽0; the case when the irregularity is equal to the dimension minus one is studied in more detail.
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V. A. Krasnov, “Compact complex manifolds without meromorphic functions,” Matem. Zametki,17, No. 1, 119–122 (1975).
S. Iitaka, “On D dimensions of algebraic varieties,” J. Math. Soc. Japan,23, 356–373 (1971).
D. Mumford, Abelian Varieties, Oxford University Press, New York (1970).
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Translated from Matematicheskie Zametki, Vol. 20, No. 2, pp. 207–214, August, 1976.
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Krasnov, V.A. The Albanese map for manifolds without meromorphic functions. Mathematical Notes of the Academy of Sciences of the USSR 20, 675–679 (1976). https://doi.org/10.1007/BF01155873
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DOI: https://doi.org/10.1007/BF01155873