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Global spherical tropicalization via toric embeddings

  • Evan D. NashEmail author
Article
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Abstract

The first steps in defining tropicalization for spherical varieties have been taken in the last few years. There are two parts to this theory: tropicalizing subvarieties of homogeneous spaces and tropicalizing their closures in spherical embeddings. In this paper, we obtain a new description of spherical tropicalization that is equivalent to the other theories. This works by embedding in a toric variety, tropicalizing there, and then applying a particular piecewise projection map. We use this theory to prove that taking closures commutes with the spherical tropicalization operation.

Notes

Acknowledgements

The author thanks Gary Kennedy for suggesting this direction of research and numerous discussions. Thanks also to Giuliano Gagliardi for providing input on several points.

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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsThe Ohio State UniversityColumbusUSA

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