Comptes Rendus
no. 9-10
Complex Analysis/Analytic Geometry
Bott–Chern cohomology and q-complete domains
[Cohomologie de Bott–Chern et domaines q-complets]

Présenté par : Jean-Pierre Demailly

Daniele Angella1 ; Simone Calamai2
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
Comptes Rendus. Mathématique, Volume 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
Daniele Angella 1 ; Simone Calamai 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 
@article{CRMATH_2013__351_9-10_343_0,
     author = {Daniele Angella and Simone Calamai},
     title = {Bott{\textendash}Chern cohomology and \protect\emph{q}-complete domains},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {343--348},
     publisher = {Elsevier},
     volume = {351},
     number = {9-10},
     year = {2013},
     doi = {10.1016/j.crma.2013.05.006},
     language = {en},
}
TY  - JOUR
AU  - Daniele Angella
AU  - Simone Calamai
TI  - Bott–Chern cohomology and q-complete domains
JO  - Comptes Rendus. Mathématique
PY  - 2013
SP  - 343
EP  - 348
VL  - 351
IS  - 9-10
PB  - Elsevier
DO  - 10.1016/j.crma.2013.05.006
LA  - en
ID  - CRMATH_2013__351_9-10_343_0
ER  - 
%0 Journal Article
%A Daniele Angella
%A Simone Calamai
%T Bott–Chern cohomology and q-complete domains
%J Comptes Rendus. Mathématique
%D 2013
%P 343-348
%V 351
%N 9-10
%I Elsevier
%R 10.1016/j.crma.2013.05.006
%G en
%F CRMATH_2013__351_9-10_343_0
Daniele Angella; Simone Calamai. Bott–Chern cohomology and q-complete domains. Comptes Rendus. Mathématique, Volume 351 (2013) no. 9-10, pp. 343-348. doi : 10.1016/j.crma.2013.05.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.05.006/

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

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

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

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

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

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

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

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

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

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

[12] M. Schweitzer 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.

Commentaires - Politique

Ces articles pourraient vous intéresser

On semistable vector bundles over curves

Indranil Biswas; Georg Hein; Norbert Hoffmann

C. R. Math (2008)