Skip to Main Content

Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2024 MCQ for Bulletin of the American Mathematical Society is 0.84.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
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 1269718
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 1328251
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 1115626
4.
G. Ellingsrud, S. Strømme, Bott's formula and enumerative geometry, J. Am. Math. Soc. 9, No.1 (1996), 175-193. MR 1317230
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 1011353
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 1653024
8.
S. Katz, On the finiteness of rational curves on quintic threefolds, Compos. Math. 60 (1986), 151-162. MR 0868135
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 1363062
10.
B. Lian, K. Liu and S.-T. Yau, Mirror principle I, Asian J. Math. 1, No.4 (1997), 729-763. MR 1621573
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 1201748
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 1191426

Review Information:

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