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Boundary manifolds of projective hypersurfaces

Domenii publicaţii > Matematica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: D. C. Cohen, A. I. Suciu

Editorial: Advances in Mathematics, 206 (2), p.538-566, 2006.


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.

Cuvinte cheie: Complex hypersurface, hyperplane arrangement, boundary manifold, cohomology ring, topological complexity, resonance variety