Vol. 90, No. 2, 1980

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On the degeneracy of a spectral sequence associated to normal crossings

Gerald Leonard Gordon

Vol. 90 (1980), No. 2, 389–396

Let W be a complex analytic manifold and V a divisor with normal crossings, and consider the Leray spectral sequence associated to the inclusion map of W V into W. We give two homological reformulations for any of the drp,q to be the zero map for r 2. These conditions are shown to be satisfied if W is compact Kähler, but it is easy to give examples when it does not degenerate at E3 if W is only a differentiable manifold. The nondegeneracy at E3 for arbitrary V in a compact Kähler manifold is interpreted in terms of reiterated residues.

Mathematical Subject Classification 2000
Primary: 32C35
Secondary: 14C30
Received: 10 July 1978
Published: 1 October 1980
Gerald Leonard Gordon