Complex Analysis/Analytic Geometry
Bott–Chern cohomology and q-complete domains
[Cohomologie de Bott–Chern et domaines q-complets]
Comptes Rendus. Mathématique, Tome 351 (2013) no. 9-10, pp. 343-348.

Dans lʼétude des cohomologies de Bott–Chern et dʼAeppli pour les varietés q-complètes, nous introduisons la classe des varietés cohomologiquement Bott–Chern q-complètes.

In studying the Bott–Chern and Aeppli cohomologies for q-complete manifolds, we introduce the class of cohomologically Bott–Chern q-complete manifolds.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.05.006
Angella, Daniele 1 ; Calamai, Simone 2

1 Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127, Pisa, Italy
2 Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126, Pisa, Italy
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Angella, Daniele; Calamai, Simone. Bott–Chern cohomology and q-complete domains. Comptes Rendus. Mathématique, Tome 351 (2013) no. 9-10, pp. 343-348. doi : 10.1016/j.crma.2013.05.006. http://www.numdam.org/articles/10.1016/j.crma.2013.05.006/

[1] Aeppli, A. On the cohomology structure of Stein manifolds, Minneapolis, MN, 1964, Springer, Berlin (1965), pp. 58-70

[2] Andreotti, A.; Grauert, H. Théorème de finitude pour la cohomologie des espaces complexes, Bull. Soc. Math. Fr., Volume 90 (1962), pp. 193-259

[3] Andreotti, A.; Vesentini, E.; Andreotti, A.; Vesentini, E. Erratum to: Carleman estimates for the Laplace–Beltrami equation on complex manifolds, Inst. Hautes Études Sci. Publ. Math., Volume 25 (1965), pp. 81-130

[4] Angella, D.; Tomassini, A. On the ¯-lemma and Bott–Chern cohomology, Invent. Math., Volume 192 (2013) no. 1, pp. 71-81

[5] Bott, R.; Chern, S.S. Hermitian vector bundles and the equidistribution of the zeroes of their holomorphic sections, Acta Math., Volume 114 (1965) no. 1, pp. 71-112

[6] Demailly, J.-P. Complex analytic and differential geometry, 2012 http://www-fourier.ujf-grenoble.fr/~demailly/manuscripts/agbook.pdf

[7] Eastwood, M.G.; Vigna Suria, G. Cohomologically complete and pseudoconvex domains, Comment. Math. Helv., Volume 55 (1980) no. 3, pp. 413-426

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

[9] Grauert, H.; Remmert, R. Theory of Stein Spaces, Grundlehren Math. Wiss., vol. 236, Springer, 2004 (reprint of the 1979 edition, originally published as)

[10] McCleary, J. A Userʼs Guide to Spectral Sequences, Cambridge Stud. Adv. Math., vol. 58, Cambridge University Press, Cambridge, 2001

[11] Rothstein, W. Zur Theorie der analytischen Mannigfaltigkeiten im Raume von n komplexen Veränderlichen, Math. Ann., Volume 129 (1955) no. 1, pp. 96-138

[12] Schweitzer, M. Autour de la cohomologie de Bott–Chern | arXiv

Cité par Sources :

This work was supported by the Project PRIN “Varietà reali e complesse: geometria, topologia e analisi armonica”, by the Project FIRB “Geometria Differenziale e Teoria Geometrica delle Funzioni”, and by GNSAGA of INdAM.