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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

A Calabi-Yau threefold with Brauer group $ (\mathbb{Z}/8\mathbb{Z})^2$

Author(s): Mark Gross; Simone Pavanelli
Journal: Proc. Amer. Math. Soc. 136 (2008), 1-9.
MSC (2000): Primary 14J32
Posted: October 11, 2007
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Abstract: We compute the Brauer group of a Calabi-Yau threefold discovered by the first author and Sorin Popescu, and find it is $ (\mathbb{Z}/8 \mathbb{Z})^2$, the largest known Brauer group of a non-singular Calabi-Yau threefold.


References:

1.
Alexeev, V., and Nakamura, I., On Mumford's construction of degenerating abelian varieties, Tohoku Math. J. (2) 51 (1999), 399-420. MR 1707764 (2001g:14013)

2.
Artin, M., Néron models, in: Arithmetic geometry (Storrs, Conn., 1984), 213-230, Springer, New York, 1986. MR 0861977

3.
Aspinwall, P., and Morrison, D., Stable singularities in string theory, with an appendix by M. Gross, Comm. Math. Phys. 178 (1996), 115-134. MR 1387944 (97d:32049)

4.
Batyrev, V., and Kreuzer, M., Integral cohomology and mirror symmetry for Calabi-Yau 3-folds, preprint, math.AG/0505432.

5.
Bayer, D., and Stillman, M., Macaulay: A system for computation in algebraic geometry and commutative algebra. Source and object code available for Unix and Macintosh computers. Contact the authors, or download from http://math.columbia.edu/ bayer/Macaulay.

6.
Bosch, S, Lütkebohmert, W., and Raynaud, M., Néron models. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 21. Springer-Verlag, Berlin, 1990.MR 1045822 (91i:14034)

7.
Caldararu, A., Derived categories of twisted sheaves on Calabi-Yau manifolds, Ph.D. thesis, Cornell University, 2000.

8.
Caldararu, A., Derived categories of twisted sheaves on elliptic threefolds, J. Reine Angew. Math. 544 (2002), 161-179.MR 1887894 (2003a:14022)

9.
Deligne, P., Théorie de Hodge. II, Inst. Hautes Études Sci. Publ. Math. No. 40 (1971), 5-57. MR 0498551 (58:16653a)

10.
Grayson, D., and Stillman, M., Macaulay 2: A computer program designed to support computations in algebraic geometry and computer algebra. Source and object code available from http://www.math.uiuc.edu/Macaulay2/.

11.
Gross, M., Special Lagrangian Fibrations I: Topology, in: Integrable Systems and Algebraic Geometry, (M.-H. Saito, Y. Shimizu and K. Ueno eds.), World Scientific 1998, 156-193.MR 1672120 (2000e:14066)

12.
Gross, M., Special Lagrangian Fibrations II: Geometry, in: Surveys in Differential Geometry, Somerville: MA, International Press 1999, 341-403.MR 1772274 (2001j:53065)

13.
Gross, M., Topological Mirror Symmetry, Invent. Math. 144 (2001), 75-137. MR 1821145 (2002c:14062)

14.
Gross, M., and Popescu, S., Equations of $ (1,d)$-polarized abelian surfaces, Math. Ann. 310 (1998), 333-377. MR 1602020 (99d:14046)

15.
Gross, M., and Popescu, S., Calabi-Yau threefolds and moduli of abelian surfaces. I Compositio Math. 127 (2001), 169-228. MR 1845899 (2002f:14057)

16.
Hulek, K., and Weintraub, S., The principal degenerations of abelian surfaces and their polarisations, Math. Ann. 286 (1990), 281-307.MR 1032935 (91e:14042)

17.
Pavanelli, S., Mirror symmetry for a two parameter family of Calabi-Yau three-folds with Euler characteristic 0, Ph.D thesis, University of Warwick, 2003.

18.
Shimura, G., Introduction to the arithmetic theory of automorphic functions, Publ. of the Math. Soc. of Japan, 11. Kanô Memorial Lectures, 1. Princeton University Press, Princeton, NJ, 1994.MR 1291394 (95e:11048)

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Additional Information:

Mark Gross
Affiliation: Department of Mathematics, University of California-San Diego, 9500 Gilman Drive, La Jolla, California 92093-0112
Email: mgross@math.ucsd.edu

Simone Pavanelli
Affiliation: Nextra Investment Management SGR, Piazza Cadorna 3, 20123 Milano, Italy
Email: simone_pavanelli@hotmail.com

DOI: 10.1090/S0002-9939-07-08840-5
PII: S 0002-9939(07)08840-5
Received by editor(s): December 14, 2005
Received by editor(s) in revised form: July 10, 2006
Posted: October 11, 2007
Additional Notes: This work was partially supported by NSF grant 0204326 and 0505325.
Communicated by: Michael Stillman
Copyright of article: Copyright 2007, American Mathematical Society


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