Abelian Varieties, Theta Functions And The Fourier Transform - 00 edition

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.

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