Abelian Varieties, Theta Functions and the Fourier Transform
£111.00
Part of Cambridge Tracts in Mathematics
- Author: Alexander Polishchuk, Boston University
- Date Published: June 2003
- availability: Available
- format: Hardback
- isbn: 9780521808040
£
111.00
Hardback
Other available formats:
eBook
Looking for an inspection copy?
This title is not currently available on inspection
-
The aim of this book is to present 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. The author starts by discussing the classical theory of theta functions from the point of view 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, the Fourier–Mukai transform can often be used to simplify the existing proofs or to provide completely new proofs of many important theorems. Graduate students and researchers with strong interest in algebraic geometry will find much of interest in this volume.
Read more- 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
Reviews & endorsements
'The book is written by a leading expert in the field and it will certainly be a valuable enhancement to the existing literature.' EMS Newsletter
Customer reviews
Not yet reviewed
Be the first to review
Review was not posted due to profanity
×Product details
- Date Published: June 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
References.
Related Books
related journals
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org
Register Sign in» Proceed
You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.
Continue ×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.
×