Skip to content
Register Sign in Wishlist
Abelian Varieties, Theta Functions and the Fourier Transform

Abelian Varieties, Theta Functions and the Fourier Transform

$131.00 (C)

Part of Cambridge Tracts in Mathematics

  • Date Published: April 2003
  • availability: Available
  • format: Hardback
  • isbn: 9780521808040

$ 131.00 (C)

Add to cart Add to wishlist

Other available formats:

Looking for an examination copy?

This title is not currently available for examination. However, if you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact providing details of the course you are teaching.

Product filter button
About the Authors
  • This book is a modern treatment of the theory of theta functions in the context of algebraic geometry. The novelty of its approach lies in the systematic use of the Fourier-Mukai transform. Alexander Polishchuk starts by discussing the classical theory of theta functions from the viewpoint of the representation theory of the Heisenberg group (in which the usual Fourier transform plays the prominent role). He then shows that in the algebraic approach to this theory (originally due to Mumford) the Fourier-Mukai transform can often be used to simplify the existing proofs or to provide completely new proofs of many important theorems. This incisive volume is for graduate students and researchers with strong interest in algebraic geometry.

    • A modern treatment of the theory of theta functions in the context of algebraic geometry
    • Discusses the classical theory of theta functions from the view of representation theory of the Heisenberg group
    • Ideal for graduate students and researchers with interest in algebraic geometry
    Read more

    Reviews & endorsements

    "I would definitely recommend this book to a reader already acquainted with abelian varieties wishing to go beyond the basics of the subject. It is stimulatig and provocative and at the same time well-organized. Even the expert will learn a lot from reading it." Bulletin of the AMS

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Date Published: April 2003
    • format: Hardback
    • isbn: 9780521808040
    • length: 308 pages
    • dimensions: 229 x 152 x 21 mm
    • weight: 0.62kg
    • contains: 88 exercises
    • availability: Available
  • Table of Contents

    Part I. Analytic Theory:
    1. Line bundles on complex tori
    2. Representations of Heisenberg groups I
    3. Theta functions
    4. Representations of Heisenberg groups II: intertwining operators
    5. Theta functions II: functional equation
    6. Mirror symmetry for tori
    7. Cohomology of a line bundle on a complex torus: mirror symmetry approach
    Part II. Algebraic Theory:
    8. Abelian varieties and theorem of the cube
    9. Dual Abelian variety
    10. Extensions, biextensions and duality
    11. Fourier–Mukai transform
    12. Mumford group and Riemann's quartic theta relation
    13. More on line bundles
    14. Vector bundles on elliptic curves
    15. Equivalences between derived categories of coherent sheaves on Abelian varieties
    Part III. Jacobians:
    16. Construction of the Jacobian
    17. Determinant bundles and the principle polarization of the Jacobian
    18. Fay's trisecant identity
    19. More on symmetric powers of a curve
    20. Varieties of special divisors
    21. Torelli theorem
    22. Deligne's symbol, determinant bundles and strange duality
    Bibliographical notes and further reading

  • Author

    Alexander Polishchuk, Boston University

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.