Available in electronic format
Available in print format
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
     

Book Review

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

Retrieve article in: PDF DVI PostScript

Book Information

Author(s): Christian Meyer
Title: Modular Calabi-Yau threefolds
Additional book information: American Mathematical Society, Providence, RI, 2005, ix+194, US$59.00, 978-0-8218-3908-9


References:

1.
G. Bini, C. De Concini, M. Polito, C. Procesi, On the work of Givental relative to mirror symmetry, math.AG/9805097.

2.
C. Breuil, B. Conrad, F. Diamond, R. Taylor, On the modularity of elliptic curves over $ \mathbf{Q}$: wild 3-adic exercises. J. Amer. Math. Soc. 14 (2001), 843-939. MR 1839918 (2002d:11058)

3.
P. Candelas, X.C. de la Ossa, P.S. Green, L. Parkes, An exactly soluble superconformal theory from a mirror pair of Calabi-Yau manifolds, Phys. Lett. B 258 (1991), no. 1-2, 118-126. MR 1101784 (93b:32028)

4.
D. Cox and S. Katz, Mirror Symmetry and Algebraic Geometry, Mathematical Surveys and Monographs 68, AMS, Providence, RI, 1999. MR 1677117 (2000d:14048)

5.
P. Deligne, Formes modulaires et représentations $ l$-adiques, In Sem. Bourbaki 355 (1968/69), Lect. Notes Math. 179 (1971).

6.
P. Deligne, La conjecture de Weil. I, Inst. Hautes Études Sci. Publ. Math. 43 (1974), 273-307. MR 0340258 (49:5013)

7.
P. Deligne, La conjecture de Weil. II. Inst. Hautes Études Sci. Publ. Math. 52 (1980), 137-252. MR 601520 (83c:14017)

8.
L. Dieulefait and J. Manoharmayum, Modularity of rigid Calabi-Yau threefolds over $ \mathbf{Q}$, In Calabi-Yau Varieties and Mirror Symmetry (Toronto, ON, 2001), Fields Inst. Commun. 38, Amer. Math. Soc., Providence, RI, 2003, 159-166. MR 2019150 (2004m:11081)

9.
J.M. Fontaine and M. Mazur, Geometric Galois representations, In Elliptic Curves, Modular Forms and Fermat's Last Theorem (Hong Kong, 1993), J. Coates, S.-T. Yau (eds.), International Press (1995), 41-78. MR 1363495 (96h:11049)

10.
A. Givental, Equivariant Gromov-Witten invariants, Internat. Math. Res. Notices, 1996, no. 13, 613-663. MR 1408320 (97e:14015)

11.
B. Greene, The Elegant Universe, W. W. Norton $ \&$ Company, Inc., New York (1999). MR 1700770 (2000f:81001)

12.
K. Hulek, R. Kloosterman, M. Schuett, Modularity of Calabi-Yau varieties, math.AG/0601238.

13.
C. Khare and J.-P. Wintenberger, Serre's modularity conjecture (I), (II), preprints.

14.
E. Lee, A modular non-rigid Calabi-Yau threefold, math.AG/0508127.

15.
B. Lian, K. Liu, S.-T. Yau, Mirror principle I, Asian J. Math. 1 (1997), 729-763. MR 1621573 (99e:14062)

16.
C.-C. Liu, K. Liu, J. Zhou, A proof of a conjecture of Mariño-Vafa on Hodge integrals, J. Differential Geom. 65 (2003), no. 2, 289-340. MR 2058264 (2005m:14104)

17.
R. Pandhripande, Rational curves on hypersurfaces (after A. Givental), Asterisque 252 (1998), 307-340. MR 1685628 (2000e:14094)

18.
M.-H. Saito and N. Yui, The modularity conjecture for rigid Calabi-Yau threefolds over $ \mathbf{Q}$, J. Math. Kyoto Univ. 41 (2001), 403-419. MR 1852991 (2002k:11102)

19.
J-P. Serre, Sur les représentations modulaires de degré 2 de Gal $ (\overline{\mathbf{Q}}/\mathbf{Q})$, Duke Math. J. 54 (1987), 179-230. MR 885783 (88g:11022)

20.
R. Taylor, Galois representations, Ann. Fac. Sci. Toulouse Math. (6) 13 (2004), 73-119. MR 2060030 (2005a:11071)

21.
S.-T. Yau, Calabi's Conjecture and Some New Results in Algebraic Geometry, Proceedings of the National Academy of Sciences 74 (1977), no. 5, 1798-1799. MR 0451180 (56:9467)


Additional Information:

Reviewer(s):
Kefeng Liu
Affiliation: Zhejiang University and University of California at Los Angeles
Email: liu@math.ucla.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 45 (2008), 163-168.

MSC (2000): Primary 14J32, 14G10, 11G25; Secondary 14E05, 14G15, 11G40
PII: S 0273-0979(07)01155-X
Posted: April 27, 2007
Additional notes: The author is supported by NSF.
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google