Résultats sur les d’d” et d”-cohomologies. Applications à l’intégration sur les cycles analytiques. II. (Some results on \(\partial {\bar\partial}\)-cohomology and \({\bar\partial}\)-cohomology. Application to the integration on analytic cycles. II). (French) Zbl 0588.32012

Ofman, Salomon

C. R. Acad. Sci., Paris, Sér. I 300, 133-135 (1985).

This paper is a continuation of a preceding note [ibid. 300, 43-45 (1985; Zbl 0584.32017)], wherein the author calculates, among other things, the dimension of the homology space belonging to a complex \[ H^ q(Y,\Omega^{q-1})\to^{d}H^ q(Y,\Omega^ q)\to^{i}V^{q,q}(Y), \] i being the natural map that associates to a \({\bar \partial}\)- cohomology class the corresponding \(\partial {\bar \partial}\)-cohomology class in the Andreotti-Norguet space \(V^{q,q}(Y)\). Here \(Y=Z\setminus X\), where Z is a compact Kähler manifold and X is a submanifold. Several applications and special cases are stated.

Reviewer: E.J.Akutowicz

MSC:

32C35	Analytic sheaves and cohomology groups
58A10	Differential forms in global analysis
14F40	de Rham cohomology and algebraic geometry
32C30	Integration on analytic sets and spaces, currents
32Q99	Complex manifolds

Keywords:

holomorphic differential forms; integrals over analytic cycles; \({\bar \partial }\)-cohomology; \(\partial {\bar \partial }\)-cohomology; Andreotti-Norguet space

Citations:

Zbl 0584.32017