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Degenerations of real irrational toric varieties

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posted on 02.06.2017, 12:16 by Elisa Postinghel, Frank Sottile, Nelly Villamizar
© 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.

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School

  • Science

Department

  • Mathematical Sciences

Published in

Journal of the London Mathematical Society

Volume

92

Issue

2

Pages

223 - 241

Citation

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.

Publisher

© The London Mathematical Society. Published by Wiley

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2015-08-04

Notes

This 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.

ISSN

0024-6107

eISSN

1469-7750

Language

en

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