Boundary manifolds of projective hypersurfaces

Details Boundary manifolds of projective hypersurfaces Boundary manifolds of projective hypersurfaces

2005-02-24

arxiv.org/abs/math/0502506v2

Advances in Mathematics 206 (2006), no. 2, 538-566

Mathematics

Algebraic Topology

31 pages; accepted for publication in Advances in Mathematics

Scientific paper

10.1016/j.aim.2005.10.003

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.

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