Cohomological aspects in complex non-Kähler geometry [electronic resource] / Daniele Angella.

Cohomological aspects in complex non-Kähler geometry [electronic resource] / Daniele Angella.

9783319024417 electronic book
3319024418 electronic book
9783319024400
331902440X

Cham : Springer, 2014.

English

1 online resource (xxv, 262 pages) : illustrations.

10.1007/978-3-319-02441-7 doi

QA331

515/.946

In these notes, we provide a summary of recent results on the cohomological properties of compact complex manifolds not endowed with a Kahler structure. On the one hand, the large number of developed analytic techniques makes it possible to prove strong cohomological properties for compact Kahler 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 Kahler 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.

Includes bibliographical references and index.

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Description based on online resource; title from PDF title page (SpringerLink, viewed November 25, 2013).

Lecture notes in mathematics (Springer-Verlag) ; 2095.

Original 9783319024400

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