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Book Review
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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:
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- 1.
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- 2.
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: 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
-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
, 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
, 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
, 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)
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- 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.
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