×

zbMATH — the first resource for mathematics

Cohomology of q-convex spaces in top degrees. (English) Zbl 0682.32017
It is shown that every strongly q-complete subvariety of a complex analytic space has a fundamental system of strongly q-complete neighborhoods. As a consequence, we find a simple proof of Ohsawa’s result that every non compact irreducible n-dimensional analytic space is strongly n-convex. An elementary proof of the existence of Hodge decomposition in top degrees for absolutely q-convex manifolds is also given.
Reviewer: J.P.Demailly

MSC:
32F10 \(q\)-convexity, \(q\)-concavity
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] [A-G] Andreotti, A., Grauert, H.: Théorèmes de finitude pour la cohomologie des espaces complexes. Bull. Soc. Math. Fr.90, 193–259 (1962) · Zbl 0106.05501
[2] [Ba] Barlet, D.: Convexité de l’espace des cycles. Bull. Soc. Math. Fr.106, 373–397 (1978) · Zbl 0395.32009
[3] [G-R] Grauert, H., Riemenschneider, O.: Kählersche Mannigfaltigkeiten mit hype-q-konvexem Rand. Problems in analysis: a Symposium in honor of Salomon Bochner. Princeton, Princeton University Press 1970
[4] [G-W] Greene, R. E., Wu, H.: Embedding of open riemannian manifolds by harmonic functions. Ann. Inst. Fourier25, 215–235 (1975) · Zbl 0307.31003
[5] [Ma] Malgrange, B.: Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution. Ann. Inst. Fourier6, 271–355 (1955/1956) · Zbl 0071.09002
[6] [Oh1] Ohsawa, T.: A reduction theorem for cohomology groups of very stronglyq-convex Kähler manifolds. Invent. Math.63, 335–354 (1981)/66, 391–393 (1982) · Zbl 0457.32007 · doi:10.1007/BF01393882
[7] [Oh2] Ohsawa, T.: Completeness of noncompact analytic spaces. Publ. R.I.M.S., Kyoto Univ.20, 683–692 (1984) · Zbl 0568.32008 · doi:10.2977/prims/1195181418
[8] [O-T] Ohsawa, T., Takegoshi, K.: Hodge spectral sequence on pseudoconvex domains. Math. Z.197, 1–12 (1988) · Zbl 0638.32016 · doi:10.1007/BF01161626
[9] [S1] Siu, Y. T.: Analytic sheaf cohomology groups of dimensionn ofn-dimensional noncompact complex manifolds. Pac. J. Math.28, 407–411 (1969)
[10] [S2] Siu, Y. T.: Analytic sheaf cohomology groups of dimensionn ofn-dimensional complex spaces. Trans. Am. Math. Soc.143, 77–94 (1969)
[11] [S3] Siu, Y.T.: Every Stein subvariety has a Stein neighborhood. Invent. Math.38, 89–100 (1976) · Zbl 0343.32014 · doi:10.1007/BF01390170
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.