\(d'd'',d''\)-cohomologies et intégration sur les cycles analytiques. \((d'd''\)-cohomology, \(d''\)-cohomology and integration over analytic cycles.)
\textit{A. Andréotti} and \textit{F. Norguet} have shown [Ann. Sc. Norm. Sup. Pisa, Sci. Fis. Mat., III. Ser. 25, 59-114 (1971; Zbl 0212.537)] that for a projective manifold Z and a smooth complete intersection X in Z of codimension \(q+1,\) the cohomology classes from \(H^ q(Z-X,\Omega^ q)\) which give identically o when integrated over (all) compact complex q- cycles of \(Z-X,\) are, up to a otier and \textit{M. Schneider} [Invent. Math. 87, 573-586 (1987; Zbl 0618.14023)] shows, even when \(\Gamma^ aE=S^ kE\) and \(p=n\), one requires at least \(\ell \geq 1\). The method of proof is to represent \(\Gamma^ aE\) as the direct image of a positive line bundle over a suitable flag manifold of E and to apply a generalization of Le Potier's isomorphism theorem to this situation. In order to overcome a difficulty arising from the fact that, when \(p<n\), the generalized Borel- Le Potier spectral sequence does not degenerate at the \(E_ 1\) level, the author obtains a new curvature estimate for the bundle of X-relative differential forms on the flag manifold of E.
scientific article; zbMATH DE number 4061632