Abelian varieties, theta functions and the fourier transform /
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge :
Cambridge University,
2003.
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| Series: | Cambridge tracts in mathematics ;
153 |
| Subjects: |
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.