Orientability of real toric varieties

Details Orientability of real toric varieties Orientability of real toric varieties

2011-02-15

arxiv.org/abs/1102.3045v1

Mathematics

Algebraic Geometry

8 pages

Scientific paper

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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