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Book Review

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Book Information:

Author: Alexander Polishchuk
Title: Abelian varieties, theta functions and the Fourier transform
Additional book information: Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge (UK), 2003, xvi+292 pp., ISBN 0-521-80804-9, £48.00

References [Enhancements On Off] (What's this?)

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  • 2. C. Birkenhake, H. Lange Complex abelian varieties, 2nd edition. Grund. Math. Wiss. 302. Springer-Verlag, Berlin (2004). MR 2062673 (2005c:14001)
  • 3. P. Cartier, Quantum mechanical commutation relations and theta functions. Algebraic Groups and Discontinuous Subgroups, pp. 361-383; Proc. Sympos. Pure Math. 9, Amer. Math. Soc., Providence (1966). MR 0216825 (35:7654)
  • 4. P. Griffiths, J. Harris, Principles of algebraic geometry. Wiley, New York (1978). MR 1288523 (95d:14001)
  • 5. C. Houzel, Fonctions elliptiques et intégrales abéliennes. Abrégé d'histoire des mathématiques 1700-1900, pp. 1-113. Hermann, Paris (1978). MR 0504183 (80k:01002b)
  • 6. S. Lefschetz, On certain numerical invariants of algebraic varieties with application to abelian varieties, Trans. Amer. Math. Soc. 22 (1921), 327-482. MR 1501178
  • 7. S. Mukai, Duality between $D(X)$ and $D(\hat X)$ with its application to Picard sheaves. Nagoya Math. J. 81 (1981), 153-175. MR 0607081 (82f:14036)
  • 8. D. Mumford, Abelian varieties. Oxford University Press, London (1970). MR 0282985 (44:219)
  • 9. D. Mumford, On the equations defining abelian varieties, I, II, III. Invent. Math. 1 (1966) 287-354; 3 (1967) 75-135 and 215-244. MR 0204427 (34:4269), MR 0219541 (36:2621), MR 0219542 (36:2622)
  • 10. D. Orlov, Equivalences of derived categories and K3 surfaces, Algebraic geometry, 7. J. Math. Sci. (New York) 84 (1997), 1361-1381. MR 1465519 (99a:14054)
  • 11. E. Picard, Sur les intégrales de différentielles totales algébriques de première espèce, J. de Math. Pures et Appliquées (4) 1 (1885), 281-346.
  • 12. E. Picard, H. Poincaré, Sur un théorème de Riemann relatif aux fonctions de $n$ variables indépendantes admettant $2n$systèmes de périodes, C.R. Acad. Sci. Paris 97 (1883), 1284-1287.
  • 13. B. Riemann, Theorie der Abel'schen Functionen, J. reine angew. Math. 54 (1857), 115-155.
  • 14. G. Scorza, Intorno alla teoria generale delle matrici di Riemann e ad alcune sue applicazioni, Rend. del Circolo Mat. di Palermo 41 (1916), 263-380.
  • 15. A. Weil, Variétés abéliennes et courbes algébriques. Hermann, Paris (1948). MR 0029522 (10:621d)
  • 16. A. Weil, Sur certains groupes d'opérateurs unitaires. Acta Math. 111 (1964), 143-211. MR 0165033 (29:2324)

Review Information:

Reviewer: Arnaud Beauville
Affiliation: Université de Nice
Email: beauville@math.unice.fr
Journal: Bull. Amer. Math. Soc. 42 (2005), 529-533
MSC (2000): Primary 14K25; Secondary 14H42
Published electronically: April 7, 2005
Review copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
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