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Link to original content: http://ncatlab.org/nlab/show/Poincaré sheaf
Poincaré line bundle in nLab

nLab Poincaré line bundle

Contents

Context

Bundles

bundles

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

Contents

Idea

The canonical line bundle on the product of an abelian group (abelian variety) and its dual Picard scheme. Alternatively its sheaf of sections: the Poincaré sheaf.

References

The idea is briefly summarized in

Lecture notes:

  • John Meth, Kelly McKinnie, The Poincaré bundle [pdf]

Monographs:

  • Alexander Polishchuk, section 16.3 of: Abelian varieties, Theta functions and the Fourier transform, Cambridge University Press (2003) [pdf]

Discussion in differential geometry and with an eye towards of (topological and geometric) T-duality:

Last revised on September 24, 2024 at 13:37:11. See the history of this page for a list of all contributions to it.