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2011•arXiv (Cornell University)Open access

ORIENTABILITY OF REAL TORIC VARIETIES

Jenya Soprunova, Frank Sottile

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Abstract

Abstract. We characterize the orientability of an abstract real toric variety as well as the orientability of a toric subvariety of a sphere. We also determine the number of components of the smooth locus of a toric variety. These results are proven for an extension of the Davis-Januskiewicz notion of a small cover to singular spaces. We characterize the orientability of toric varieties associated to posets, and discuss an application to the study of real solutions to systems of polynomial equations.

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Abstract. We characterize the orientability of an abstract real toric variety as well as the orientability of a toric subvariety of a sphere. We also determine the number of components of the smooth locus of a toric variety. These results are proven for an extension of the Davis-Januskiewicz notion of a small cover to singular spaces. We characterize the orientability of toric varieties associated to posets, and discuss an application to the study of real solutions to systems of polynomial equations.

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Available abstract

Abstract. We characterize the orientability of an abstract real toric variety as well as the orientability of a toric subvariety of a sphere. We also determine the number of components of the smooth locus of a toric variety. These results are proven for an extension of the Davis-Januskiewicz notion of a small cover to singular spaces. We characterize the orientability of toric varieties associated to posets, and discuss an application to the study of real solutions to systems of polynomial equations.

Key concepts: Subvariety, Toric variety, Mathematics, Variety (cybernetics), Pure mathematics, Algebra over a field, Statistics

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