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Advances in Geometry

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On non-Kähler degrees of complex manifolds

Daniele Angella
  • Dipartimento di Matematica e Informatica “Ulisse Dini”, Università degli Studi di Firenze, viale Morgagni 67/a, 50134 Firenze, Italy
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/ Adriano Tomassini
  • Corresponding author
  • Dipartimento di Scienze Matematiche, Fisiche, ed Informatiche, Plesso Matematico e Informatico, Università di Parma, Parco Area delle Scienze 53/A, 43124, Parma, Italy.
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/ Misha Verbitsky
  • Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castor ina, 110, Jardim Botânico, CEP 22460-320, Rio de Janeiro, RJ, Brasil
  • Laboratory of Algebraic Geometry, Faculty of Mathematics, National Research University HSE, 7 Vavilova Str. Moscow, Russia
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Published Online: 2018-10-25 | DOI: https://doi.org/10.1515/advgeom-2018-0026

Abstract

We study cohomological properties of complex manifolds. In particular, under suitable metric conditions, we extend to higher dimensions a result by A. Teleman, which provides an upper bound for the Bott– Chern cohomology in terms of Betti numbers for compact complex surfaces according to the dichotomy b1 even or odd.

Keywords: Cohomology; complex surface; non-Kähler

MSC 2010: 32Q55; 32C35; 53C55

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About the article

E-mail: daniele.angella@unifi.it


Received: 2016-12-13

Published Online: 2018-10-25


Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2018-0026.

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