On the degeneracy of a spectral sequence associated to normal crossings

Gerald Leonard Gordon

Vol. 90 (1980), No. 2, 389–396

DOI: 10.2140/pjm.1980.90.389

Abstract

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 d_r^p,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

Milestones

Received: 10 July 1978

Published: 1 October 1980