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Is Every Toric Variety an M-Variety?

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An Erratum to this article was published on 17 June 2006

Abstract

A complex algebraic variety X defined over the real numbers is called an M-variety if the sum of its Betti numbers (for homology with closed supports and coefficients in \(\mathbb{Z} /2\)) coincides with the corresponding sum for the real part of X. It has been known for a long time that any nonsingular complete toric variety is an M-variety. In this paper we consider whether this remains true for toric varieties that are singular or not complete, and we give a positive answer when the dimension of X is less than or equal to 3 or when X is complete with isolated singularities.

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Authors and Affiliations

  1. Laboratoire de Mathématiques, Université de Savoie, 73376, Le Bourget-du-Lac Cedex, France

    Frédéric Bihan

  2. Fachbereich Mathematik, Universität Konstanz, 78457, Konstanz, Germany

    Matthias Franz

  3. Mathematics Department, University of Georgia, Athens, GA, 30602, USA

    Clint McCrory

  4. Departement Wiskunde, K. U. Leuven, Celestijnenlaan 200B, 3001, Leuven (Heverlee), Belgium

    Joost van Bihan

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  1. Frédéric Bihan
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  2. Matthias Franz
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  3. Clint McCrory
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  4. Joost van Bihan
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An erratum to this article can be found at http://dx.doi.org/10.1007/s00229-006-0019-5

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Bihan, F., Franz, M., McCrory, C. et al. Is Every Toric Variety an M-Variety?. manuscripta math. 120, 217–232 (2006). https://doi.org/10.1007/s00229-006-0004-z

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  • DOI: https://doi.org/10.1007/s00229-006-0004-z

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