Abelian Varieties

D. Huybrechts

in Fourier-Mukai Transforms in Algebraic Geometry

Published in print April 2006 | ISBN: 9780199296866
Published online September 2007 | e-ISBN: 9780191711329 | DOI:

Series: Oxford Mathematical Monographs

Abelian Varieties

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Historically, Mukai's equivalence with the Poincare bundle on the product of an abelian variety and its dual as kernel was the fist Fourier-Mukai transform. The first section in this chapter functions as a reminder of the basic facts from the rich theory of abelian varieties, and the case of principally polarized abelian varieties is studied. A general investigation of derived equivalences between abelian varieties and derived autoequivalences of a single abelian variety is included.

Keywords: abelian varieties; principally polarized varieties; Poincare bundle

Chapter.  19346 words. 

Subjects: Geometry

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