Leray spectral sequence for complements of certain arrangements of smooth submanifolds

TL;DR

This paper investigates the Leray spectral sequence associated with the complement of certain submanifold arrangements in complex algebraic manifolds, providing conditions for its degeneration at the E_3 stage.

Contribution

It introduces a new condition ensuring the degeneration of the Leray spectral sequence for complements of submanifold arrangements with singular intersections.

Findings

Spectral sequence degenerates at E_3 under the given condition

Provides a framework for analyzing arrangements with singular intersections

Advances understanding of cohomological properties of submanifold complements

Abstract

Let Z be an arrangement of submanifolds in a complex compact algebraic manifold X. We allow some kind of singular intersections. We consider the Leray spectral sequence of the embedding of the U=X-Z into X and formulate a condition sufficient for degeneration of this spectral sequence on E_3-table.