Topological versions of Abel-Jacobi, the height pairing, and the Poincaré bundle

Details Topological versions of Abel-Jacobi, the height pairing, and the Poincaré bundle Topological versions of Abel-Jacobi, the height pairing, and the Poincaré bundle

2011-04-20

arxiv.org/abs/1104.4057v3

Mathematics

Algebraic Geometry

12 pages

Scientific paper

We extend to the topological setting the classical constructions of the Abel-Jacobi mapping on homologically trivial algebraic cycles and the height pairing between two such cycles. We further interpret the height pairing between homologically trivial topological cycles (with disjoint support) as giving a lifting of their Abel-Jacobi images to the fiber of the Poincar\'e bundle, extending work of R. Hain in the algebraic setting. The current revision corrects and extends the relationship between the topological height pairing and the classical height pairing in the case of algebraic cycles in Section 4.

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