Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

A counterexample to the maximality of toric varieties

Author(s): Valerie Hower
Journal: Proc. Amer. Math. Soc. 136 (2008), 4139-4142.
MSC (2000): Primary 14M25, 14F45; Secondary 05B35
Posted: June 17, 2008
MathSciNet review: 2431025
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Abstract | References | Similar articles | Additional information

Abstract: We present a counterexample to the conjecture of Bihan, Franz, McCrory, and van Hamel concerning the maximality of toric varieties. There exists a six dimensional projective toric variety with the sum of the $\mathbb{Z}_2$ Betti numbers of $X(\mathbb{R})$ strictly less than the sum of the $\mathbb{Z}_2$ Betti numbers of $X(\mathbb{C})$ .

References:

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[Bih]: F. Bihan, M. Franz, C. McCrory, J. van Hamel, Is every toric variety an M-variety?, Manuscripta Math. 120 (2006), 217-232. MR 2234250
[Deg]: A. Degtyarev, I. Itenberg, V. Kharlamov, Real Enriques Surfaces, Springer-Verlag, New York, 2000. MR 1795406 (2001k:14100)
[Fra]: M. Franz, Maple package $\mathtt{torhom},$ version 1.3.0, September 13, 2004, Available at http://www-fourier.ujf-grenoble.fr/franz/maple/torhom.html
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[How]: V. Hower, Hodge spaces of real toric varieties, Collect. Math. 59 (2008), 215-237.
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Additional Information:

Valerie Hower
Affiliation: Department of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
Email: vhower@math.gatech.edu

DOI: 10.1090/S0002-9939-08-09431-8
PII: S 0002-9939(08)09431-8
Received by editor(s): May 4, 2007,
Received by editor(s) in revised form: November 1, 2007
Posted: June 17, 2008
Communicated by: Ted Chinburg
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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