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ISSN 1088-9485(e) ISSN 0273-0979(p)

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 pp., US$59.00, ISBN 978-0-8218-3908-9

References:

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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)
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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)
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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.
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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)
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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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