Almost complex manifolds from the point of view of Kodaira dimension
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 a 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.
Keywords
Cite
@article{arxiv.2307.14215,
title = {Almost complex manifolds from the point of view of Kodaira dimension},
author = {Andrea Cattaneo},
journal= {arXiv preprint arXiv:2307.14215},
year = {2023}
}
Comments
12 pages. This paper is based on a talk held by the author during the workshop "Cohomology of Complex Manifolds and Special Structures, II" in July 2021