Primitive cohomology and the tube mapping

Abstract

Let X be a smooth complex projective variety of dimension d. We show that its primitive cohomology in degree d is generated by certain "tube classes," constructed from the monodromy of the family of smooth hyperplane sections on X. The proof makes use of a result about the group cohomology of certain representations that may be of independent interest.

24 pages; result now holds for arbitrary dimension; uses Paul Taylor's package for commutative diagrams

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