Chapter

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: https://dx.doi.org/10.1093/acprof:oso/9780199296866.003.0009

Series: Oxford Mathematical Monographs

Abelian Varieties

Show Summary Details

Preview

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

Full text: subscription required

How to subscribe Recommend to my Librarian

Buy this work at Oxford University Press »

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content. subscribe or login to access all content.