Abelian Varieties, Theta Functions and the Fourier Transform

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一本关于 Fourier Transform 的书，希望对读者有所帮助！

以下是目录：

Part I. Analytic Theory
1 Line Bundles on Complex Tori 3
2 Representations of Heisenberg Groups I 16
3 Theta Functions I 27
Appendix A. Theta Series and Weierstrass Sigma Function 37
4 Representations of Heisenberg Groups II: Intertwining Operators 40
Appendix B. Gauss Sums Associated with Integral Quadratic Forms 58
5 Theta Functions II: Functional Equation 61
6 Mirror Symmetry for Tori 77
7 Cohomology of a Line Bundle on a Complex Torus:
Mirror Symmetry Approach 89
Part II. Algebraic Theory
8 Abelian Varieties and Theorem of the Cube 99
9 Dual Abelian Variety 109
10 Extensions, Biextensions, and Duality 122
11 Fourier–Mukai Transform 134
12 Mumford Group and Riemann’s Quartic Theta Relation 150
13 More on Line Bundles 166
14 VectorBundles on Elliptic Curves 175
15 Equivalences between Derived Categories of Coherent
Sheaves on Abelian Varieties 183
Part III. Jacobians
16 Construction of the Jacobian 209
17 Determinant Bundles and the Principal Polarization
of the Jacobian 220
18 Fay’s Trisecant Identity 235
vii
viii Contents
19 More on Symmetric Powers of a Curve 242
20 Varieties of Special Divisors 252
21 Torelli Theorem 259
22 Deligne’s Symbol, Determinant Bundles, and Strange Duality 266
Appendix C. Some Results from Algebraic Geometry 275
Bibliographical Notes and Further Reading 279
References 283
Index 291

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关键词：transform Varieties Functions function Fourier Complex Series Sigma