© 2015 London Mathematical Society.A real irrational toric variety X is an analytic subset of the simplex associated to a finite configuration of real vectors. The positive torus acts on X by translation, and we consider limits of sequences of these translations. Our main result identifies all possible Hausdorff limits of translations of X as toric degenerations using elementary methods and the geometry of the secondary fan of the vector configuration. This generalizes work of García-Puente et al., who used algebraic geometry and work of Kapranov, Sturmfels and Zelevinsky, when the vectors were integral.
Published inJournal of the London Mathematical Society
Pages223 - 241
CitationPOSTINGHEL, E., SOTTILE, F. and VILLAMIZAR, N., 2015. Degenerations of real irrational toric varieties. Journal of the London Mathematical Society, 92(2), pp. 223-241.
Publisher© The London Mathematical Society. Published by Wiley
VersionAM (Accepted Manuscript)
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NotesThis is the peer reviewed version of the following article: POSTINGHEL, E., SOTTILE, F. and VILLAMIZAR, N., 2015. Degenerations of real irrational toric varieties. Journal of the London Mathematical Society, 92(2), pp. 223-241., which has been published in final form at http://dx.doi.org/10.1112/jlms/jdv024. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.