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Book Review

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Book Information:

Authors: David A. Cox and Sheldon Katz
Title: Mirror symmetry and algebraic geometry
Additional book information: Mathematical Surveys and Monographs, vol. 68, American Mathematical Society, Providence, RI, xxi + 469 pp., ISBN 0-8218-1059-6, $69.00

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

  • 1. V.V. Batyrev, Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties, J. Algebraic Geom. 3 (1994), 493-535. MR 95c:14046
  • 2. V.V. Batyrev and D. van Straten, Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toric varieties, Commun. Math. Phys. 168 (1995), 493-533. MR 96g:32037
  • 3. Ph. Candelas, X. de la Ossa, P. Green, L. Parkes, A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory, Nucl. Phys. B 359 (1991), 21-74. MR 93b:32029
  • 4. G. Ellingsrud, S. Strømme, Bott's formula and enumerative geometry, J. Am. Math. Soc. 9, No.1 (1996), 175-193. MR 96j:14039
  • 5. I.M. Gel'fand, A.V. Zelevinskij, M.M. Kapranov, Hypergeometric functions and toric varieties, Funct. Anal. Appl. 23, No.2 (1989), 94-106. MR 90m:22025
  • 6. A. Givental, Equivariant Gromov-Witten Invariants, Internat. Math. Res. Not., No. 13 (1996), 613-663.
  • 7. A. Givental, A Mirror Theorem for Toric Complete Intersections, in Topological field theory, primitive forms and related topics (Kashiwara, Masaki et al. eds.), Proceedings of the 38th Taniguchi symposium, Kyoto, Japan, December 9-13, 1996, Prog. Math. 160, Birkhäuser (1998), 141-175. MR 2000a:14063
  • 8. S. Katz, On the finiteness of rational curves on quintic threefolds, Compos. Math. 60 (1986), 151-162. MR 88a:14047
  • 9. M. Kontsevich, Enumeration of rational curves via torus actions, in The moduli space of curves (Dijkgraaf, R. H. et al. eds.), Proceedings of the conference held on Texel Island, 1994, Prog. Math. 129, Birkhäuser (1995), 335-368. MR 97d:14077
  • 10. B. Lian, K. Liu and S.-T. Yau, Mirror principle I, Asian J. Math. 1, No.4 (1997), 729-763. MR 99e:14062
  • 11. A. Libgober and J. Teitelbaum, Lines on Calabi-Yau complete intersections, mirror symmetry, and Picard-Fuchs equations, Int. Math. Res. Not., No.1 (1993), 29-39. MR 93k:14013
  • 12. D. Morrison, Picard-Fuchs equations and mirror maps for hypersurfaces (Yau, Shing-Tung ed.), Essays on mirror manifolds, International Press, Cambridge, MA (1992), 241-264. MR 94b:32035

Review Information:

Reviewer: V. Batyrev
Affiliation: Universität Tübingen
Email: batyrev@bastau.mathematik.uni-tuebingen.de
Journal: Bull. Amer. Math. Soc. 37 (2000), 473-476
MSC (2000): Primary 14-02; Secondary 81-02
Published electronically: June 27, 2000
Review copyright: © Copyright 2000 American Mathematical Society
American Mathematical Society