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Cohomological Aspects in Complex Non-Kaehler Geometry. 2014 ed..
・ISBN 978-3-319-02440-0 paper EUR 34.99
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| 著者・編者 | Angella, Daniele, |
|---|---|
| シリーズ | Lecture Notes in Mathematics |
| 出版社 | (Springer International Publishing AG, SZ) |
| 出版年月 | 2013 |
| ページ数 | 262 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-24441＞ |
解説
In these notes, we provide a summary of recent results on the cohomological properties of compact complex manifolds not endowed with a Kaehler structure.
On the one hand, the large number of developed analytic techniques makes it possible to prove strong cohomological properties for compact Kaehler manifolds. On the other, in order to further investigate any of these properties, it is natural to look for manifolds that do not have any Kaehler structure.
We focus in particular on studying Bott-Chern and Aeppli cohomologies of compact complex manifolds. Several results concerning the computations of Dolbeault and Bott-Chern cohomologies on nilmanifolds are summarized, allowing readers to study explicit examples. Manifolds endowed with almost-complex structures, or with other special structures (such as, for example, symplectic, generalized-complex, etc.), are also considered.