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On an example of Aspinwall and Morrison
Author(s):
Balázs
Szendroi
Journal:
Proc. Amer. Math. Soc.
132
(2004),
621-632.
MSC (2000):
Primary 14J32, 14C34, 14M25
Posted:
September 29, 2003
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Abstract:
In this paper, a family of smooth multiply-connected Calabi-Yau threefolds is investigated. The family presents a counterexample to global Torelli as conjectured by Aspinwall and Morrison.
References:
- 1.
- P. Aspinwall and D. Morrison, Chiral rings do not suffice:
 theories with nonzero fundamental group, Phys. Lett. B 334 (1994), 79-86. MR 96b:32031 - 2.
- M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes, Comm. Math. Phys. 165 (1994), 311-427. MR 95f:32029
- 3.
- D. A. Cox and S. Katz, Mirror symmetry and algebraic geometry, Mathematical Surveys and Monographs 68, American Mathematical Society, Providence, 1999. MR 2000d:14048
- 4.
- B. Fantechi and R. Pardini, Automorphisms and moduli spaces of varieties with ample canonical class via deformations of abelian covers, Comm. Algebra 25 (1997), 1413-1441. MR 98c:14028
- 5.
- W. Fulton, Introduction to toric varieties, Annals of Math. Stud. 131, Princeton University Press, Princeton, NJ, 1993. MR 94g:14028
- 6.
- P. A. Griffiths, Periods of integrals on algebraic manifolds I, Amer. J. Math. 90 (1968), 568-626. MR 37:5215
- 7.
- M. Gross, Special Lagrangian Fibrations II: Geometry. A survey of techniques in the study of special Lagrangian fibrations, in: Surveys in differential geometry: differential geometry inspired by string theory, 341-403, Surv. Differ. Geom. 5, Int. Press, Boston, MA, 1999. MR 2001j:53065
- 8.
- E. Horikawa, On the periods of Enriques surfaces I-II, Math. Ann. 234 (1978), 73-88, 235 (1978), 217-246. MR 58:10927a; MR 58:10927b
- 9.
- J. Kollár, Flops, Nagoya Math. J. 113 (1989), 15-36. MR 90e:14011
- 10.
- H. Matsumura and P. Monsky, On the automorphisms of hypersurfaces, J. Math. Kyoto Univ. 3 (1963/1964), 347-361. MR 29:5819
- 11.
- Y. Miyaoka, The Chern classes and Kodaira dimension of a minimal variety, in: Algebraic geometry, Sendai 1985 (ed. T. Oda), 449-476, Adv. Stud. Pure Math. 10, North-Holland, Amsterdam-New York, 1987. MR 89k:14022
- 12.
- Z. Ran, Unobstructedness of Calabi-Yau orbi-Kleinfolds, J. Math. Phys. 39 (1998), 625-629. MR 98m:14043
- 13.
- B. Szendroi, Calabi-Yau threefolds with a curve of singularities and counterexamples to the Torelli problem, International J. Math. 11 (2000), 449-459. MR 2002a:14045
- 14.
- B. Szendroi, On a conjecture of Cox and Katz, Math. Z. 240 (2002), 233-241. MR 2003c:14043
- 15.
- P. Tzermias, The group of automorphisms of the Fermat curve, J. Number Theory 53 (1995), 173-178. MR 96e:11084
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Additional Information:
Balázs
Szendroi
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
Address at time of publication:
Department of Mathematics, Utrecht University, P.O. Box 80010, NL-3508 TA Utrecht, The Netherlands -- and -- Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, Hungary
Email:
szendroi@math.uu.nl
DOI:
10.1090/S0002-9939-03-07084-9
PII:
S 0002-9939(03)07084-9
Received by editor(s):
October 25, 2001
Received by editor(s) in revised form:
July 20, 2002
Posted:
September 29, 2003
Additional Notes:
This research was partially supported by an Eastern European Research Bursary from Trinity College, Cambridge and an ORS Award from the British Government
Communicated by:
Michael Stillman
Copyright of article:
Copyright
2003,
American Mathematical Society
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