Spherical tropicalization and Berkovich analytification

2022/05/20 by Desmond Coles, Coles, Desmond · 1 citation
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics #Meromorphic and Entire Functions #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2205.09964

openalex publication_date 2022/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a spherical variety. We show that Tevelev and Vogiannou's tropicalization map from X to its tropicalization factors through the Berkovich analytification X^an, as in the case for toric varieties. Furthermore we show that the tropicalization is a strong deformation retraction of X^an. We also give a strong deformation retraction of Thuillier's analytification X^\beth onto a subspace described using the colored fan of X.

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