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arXiv · 1312.3834

Degenerations of real irrational toric varieties

Elisa Postinghel·Frank Sottile·Nelly Villamizar
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Abstract

An 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 Garcia-Puente et al., who used algebraic geometry and work of Kapranov, Sturmfels, and Zelevinsky, when the vectors were integral.

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Elisa Postinghel, Frank Sottile, Nelly Villamizar. 2013-12-13. Degenerations of real irrational toric varieties. https://doi.org/10.1112/jlms%2Fjdv024

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