Primitive cohomology and the tube mapping

Details Primitive cohomology and the tube mapping Primitive cohomology and the tube mapping

2007-11-26

arxiv.org/abs/0711.3927v2

Mathematics

Algebraic Geometry

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

Scientific paper

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.

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