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SPHERICAL TROPICALIZATION

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Abstract

We extend tropicalization and tropical compactification of subvarieties of algebraic tori to subvarieties of spherical homogeneous spaces. Given a tropical compactification of a subvariety, we show that the support of the colored fan of the ambient spherical variety agrees with the tropicalization of the subvariety. The proof is based on our equivariant version of the flattening by blow-up theorem. We provide many examples.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA, USA

    J. TEVELEV & T. VOGIANNOU

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  1. J. TEVELEV
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  2. T. VOGIANNOU
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Correspondence to T. VOGIANNOU.

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In memory of Ernest Borisovich Vinberg

J. Tevelev the project was supported by the NSF grant DMS-1701704, Simons Fellowship, and the HSE University Basic Research Program and Russian Academic Excellence Project ‘5-100’.

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TEVELEV, J., VOGIANNOU, T. SPHERICAL TROPICALIZATION. Transformation Groups 26, 691–718 (2021). https://doi.org/10.1007/s00031-021-09641-4

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