On the

Abstract

A Frölicher-type inequality for Bott-Chern cohomology and its relation with

\partial \overline{\partial }

\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\partial {{\bar{\partial }}}$$\end{document}

-lemma were introduced in [1]. In this paper, we generalize these results to the cohomology groups with coefficients in flat complex vector bundles.

Keywords

Bott-Chern cohomology /

\partial \overline{\partial }

\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\partial {{\bar{\partial }}}$$\end{document}

-lemma')">

\partial \overline{\partial }

\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\partial {{\bar{\partial }}}$$\end{document}

-lemma / Non-Kähler

References

[1] Angella D, Tomassini A. On the ∂ ∂ ¯ \documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\partial {{\bar{\partial }}}$$\end{document}-lemma and Bott-Chern cohomology. Invent. Math., 2013, 192: 71-81,

[2] Deligne P, Griffith P, Morgan J, Sullivan D. Real homotopy theory of Kähler manifolds. Invent. Math., 1975, 29(3): 245-274,

[3] Frölicher A. Relations between the cohomology groups of Dolbeault and topological invariants. Proc. Natl. Acad. Sci. USA, 1955, 41(3): 641-644, pmcid: 528153

[4] Schweitzer, M.: Autour de la cohomologie de Bott-Chern (PhD thesis), Institut Fourier, Université de Grenoble I, Grenoble, France (2007). https://www-fourier.ujf-grenoble.fr/~demailly/theses/schweitzer_bott_chern_2007.pdf

[5] Varouchas, J.: Proprietés cohomologiques d’une classe de variétés analytiques complexes compactes. In: Séminaire d’analyse P. Lelong-P. Dolbeault-H. Skoda, années 1983/1984. Lecture Notes in Math., vol. 1198, pp. 233-243. Springer, Berlin (1986). https://doi.org/10.1007/BFb0077057