The lecture provides a nice overview of the cohomology of the boundary manifold of an arrangement of hyperplanes. First, the boundary manifold is constructed. In higher dimensions the fundamental group is isomorphic to the fundamental group of the arrangement complement. The double of the Orlik-Solomon algebra is constructed by means of a trivial extension. Then using properties of the mixed Hodge structure of the Orlik-Solomon algebra it is shown that the cohomology of the boundary is isomorphic to the double of the Orlik-Solomon algebra. The lecture ends with an investigation of the resonance of the cohomology of the boundary manifold.

Keywords:

Trivial extension; resonance varieties; projective hypersurface; mixed Hodge structures.

Lecture #10657

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