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Fourier-Mukai Transforms in Algebraic Geometry$
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D. Huybrechts

Print publication date: 2006

Print ISBN-13: 9780199296866

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780199296866.001.0001

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Abelian Varieties

Abelian Varieties

(p.192) 9 Abelian Varieties
Fourier-Mukai Transforms in Algebraic Geometry

D. Huybrechts

Oxford University Press

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

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