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arXiv · 1611.01841

Gr\"obner theory and tropical geometry on spherical varieties

Kiumars Kaveh·Christopher Manon
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Abstract

Let $G$ be a connected reductive algebraic group. We develop a Gr\"obner theory for multiplicity-free $G$-algebras, as well as a tropical geometry for subschemes in a spherical homogeneous space $G/H$. We define the notion of a spherical tropical variety and prove a fundamental theorem of tropical geometry in this context. We also propose a definition for a spherical amoeba in $G/H$. Our work partly builds on the previous work of Vogiannou on spherical tropicalization and in some ways is complementary.

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Kiumars Kaveh, Christopher Manon. 2016-11-06. Gr\"obner theory and tropical geometry on spherical varieties. https://arxiv.org/abs/1611.01841

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