Riv. Mat. Univ. Parma, Vol. 13, No. 2, 2022

Andrea Cattaneo [a]

Almost complex manifolds from the point of view of Kodaira dimension

Pages: 535-549
Received: 6 December 2021
Accepted in revised form: 11 May 2022
Mathematics Subject Classification: 32Q60.
Keywords: Kodaira dimension, almost complex manifold, meromorphic function.
Author address:
[a]: Università di Parma, Dipartimento di Scienze Matematiche Fisiche e Informatiche, Unità di Matematica e Informatica, Parma, Italy

The author is a member of GNSAGA of INdAM.

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Abstract: In complex geometry a classical and useful invariant of a complex manifold is its Kodaira dimension. Since its introduction by Iitaka in the early 70's, its behavior under deformations was object of study and it is known that Kodaira dimension is invariant under holomorphic deformations for smooth projective manifolds, while there are examples of holomorphic deformations of non-projective manifolds for which the Kodaira dimension is non-constant. Recently this concept has been generalized to almost complex manifolds, we want to present here some of its main features in the non-integrable case, mainly with respect to deformations. At the end we conclude with some speculations on the theory of meromorphic functions on almost complex manifolds.

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