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.

中文翻译：

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球面热带化

我们将代数花托的亚变种的热带化和热带压实扩展到球形同质空间的亚变种。给定一个子品种的热带压实，我们证明了周围球形品种的彩色扇的支持与该子品种的热带化相吻合。证明是基于我们的爆破定理的平坦化的等变形式。我们提供了许多示例。