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A Calabi-Yau threefold with Brauer group
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 , 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
-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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