Boundary manifolds of projective hypersurfaces

Abstract

We study the topology of the boundary manifold of a regular neighborhood of a complex projective hypersurface. We show that, under certain Hodge theoretic conditions, the cohomology ring of the complement of the hypersurface functorially determines that of the boundary. When the hypersurface defines a hyperplane arrangement, the cohomology of the boundary is completely determined by the combinatorics of the underlying arrangement and the ambient dimension. We also study the LS category and topological complexity of the boundary manifold, as well as the resonance varieties of its cohomology ring.

31 pages; accepted for publication in Advances in Mathematics

References in corpus (3)

• Characteristic varieties of arrangements
• Chen Lie algebras
• Alexander Invariants of Complex Hyperplane Arrangements

Cited by in corpus (10)

• Hyperplane arrangements and Milnor fibrations
• Fundamental groups, Alexander invariants, and cohomology jumping loci
• Which 3-manifold groups are Kähler groups?
• The boundary manifold of a complex line arrangement
• Reidemeister Torsion, Peripheral Complex, and Alexander Polynomials of Hypersurface Complements
• Cohomology jump loci of 3-manifolds
• On the topology of the Milnor fibration of a hyperplane arrangement
• Spectral pairs, Alexander modules, and boundary manifolds
• Resonance varieties over fields of positive characteristic
• LS-category and sequential topological complexity of symmetric products