Abelian varieties, theta functions, and the Fourier transform / (Record no. 517879)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03325nam a22003738i 4500 |
| 001 - CONTROL NUMBER | |
| control field | CR9780511546532 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | UkCbUP |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20200124160234.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION | |
| fixed length control field | m|||||o||d|||||||| |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr|||||||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 090508s2003||||enk o ||1 0|eng|d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780511546532 (ebook) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Cancelled/invalid ISBN | 9780521808040 (hardback) |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | UkCbUP |
| Language of cataloging | eng |
| Description conventions | rda |
| Transcribing agency | UkCbUP |
| 050 00 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA564 |
| Item number | .P64 2003 |
| 082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 516.3/5 |
| Edition number | 21 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Polishchuk, Alexander, |
| Dates associated with a name | 1971- |
| Relator term | author. |
| 245 10 - TITLE STATEMENT | |
| Title | Abelian varieties, theta functions, and the Fourier transform / |
| Statement of responsibility, etc | Alexander Polishchuk. |
| 246 3# - VARYING FORM OF TITLE | |
| Title proper/short title | Abelian Varieties, Theta Functions & the Fourier Transform |
| 264 #1 - Production, Publication, Distribution, Manufacture, and Copyright Notice (R) | |
| Place of production, publication, distribution, manufacture (R) | Cambridge : |
| Name of producer, publisher, distributor, manufacturer (R) | Cambridge University Press, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2003. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (xvi, 292 pages) : |
| Other physical details | digital, PDF file(s). |
| 336 ## - Content Type (R) | |
| Content type term (R) | text |
| Content type code (R) | txt |
| Source (NR) | rdacontent |
| 337 ## - Media Type (R) | |
| Media type term (R) | computer |
| Media type code (R) | c |
| Source (NR) | rdamedia |
| 338 ## - Carrier Type (R) | |
| Carrier type term (R) | online resource |
| Carrier type code (R) | cr |
| Source (NR) | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| სერიის ცნობა | Cambridge tracts in mathematics ; |
| Volume number/sequential designation | 153 |
| 500 ## - GENERAL NOTE | |
| General note | Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Pt. I. Analytic Theory -- 1. Line Bundles on Complex Tori -- 2. Representations of Heisenberg Groups I -- 3. Theta Functions I -- App. A. Theta Series and Weierstrass Sigma Function -- 4. Representations of Heisenberg Groups II: Intertwining Operators -- App. B. Gauss Sums Associated with Integral Quadratic Forms -- 5. Theta Functions II: Functional Equation -- 6. Mirror Symmetry for Tori -- 7. Cohomology of a Line Bundle on a Complex Torus: Mirror Symmetry Approach -- Pt. 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 -- Pt. III. Jacobians -- 16. Construction of the Jacobian -- 17. Determinant Bundles and the Principal 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 -- App. C. Some Results from Algebraic Geometry. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | 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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Abelian varieties. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Fourier transformations. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Display text | Print version: |
| International Standard Book Number | 9780521808040 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Cambridge tracts in mathematics ; |
| Volume number/sequential designation | 153. |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://doi.org/10.1017/CBO9780511546532">https://doi.org/10.1017/CBO9780511546532</a> |
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