%0 Journal Article %A Postinghel, Elisa %A Sottile, Frank %A Villamizar, Nelly %D 2017 %T Degenerations of real irrational toric varieties %U https://repository.lboro.ac.uk/articles/journal_contribution/Degenerations_of_real_irrational_toric_varieties/9385511 %2 https://repository.lboro.ac.uk/ndownloader/files/16998710 %K untagged %K Mathematical Sciences not elsewhere classified %X © 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. %I Loughborough University