000			03325nam a22003738i 4500
001			CR9780511546532
003			UkCbUP
005			20200124160234.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			090508s2003||||enk o ||1 0|eng|d
020			_a9780511546532 (ebook)
020			_z9780521808040 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA564 _b.P64 2003
082	0	0	_a516.3/5 _221
100	1		_aPolishchuk, Alexander, _d1971- _eauthor.
245	1	0	_aAbelian varieties, theta functions, and the Fourier transform / _cAlexander Polishchuk.
246	3		_aAbelian Varieties, Theta Functions & the Fourier Transform
264		1	_aCambridge : _bCambridge University Press, _c2003.
300			_a1 online resource (xvi, 292 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aCambridge tracts in mathematics ; _v153
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_aPt. 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			_aThe 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	_aAbelian varieties.
650		0	_aFourier transformations.
776	0	8	_iPrint version: _z9780521808040
830		0	_aCambridge tracts in mathematics ; _v153.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511546532
999			_c517879 _d517877