GRÖBNER THEORY AND TROPICAL GEOMETRY ON SPHERICAL VARIETIES

Kiumars Kaveh; Christopher Manon

doi:10.1007/s00031-019-09536-5

GRÖBNER THEORY AND TROPICAL GEOMETRY ON SPHERICAL VARIETIES

Kiumars Kaveh
, Christopher Manon

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Let G be a connected reductive algebraic group. We develop a Gröbner 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 using Cartan decomposition. Our work partly builds on the previous work of Vogiannou on spherical tropicalization and in some ways is complementary.

Original language	English
Pages (from-to)	1095-1145
Number of pages	51
Journal	Transformation Groups
Volume	24
Issue number	4
DOIs	https://doi.org/10.1007/s00031-019-09536-5
State	Published - Dec 1 2019

Bibliographical note

Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.

Funding

Funders	Funder number
National Science Foundation Arctic Social Science Program	1500966

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology

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10.1007/s00031-019-09536-5

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abstract = "Let G be a connected reductive algebraic group. We develop a Gr{\"o}bner 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 using Cartan decomposition. Our work partly builds on the previous work of Vogiannou on spherical tropicalization and in some ways is complementary.",

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N2 - Let G be a connected reductive algebraic group. We develop a Gröbner 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 using Cartan decomposition. Our work partly builds on the previous work of Vogiannou on spherical tropicalization and in some ways is complementary.

AB - Let G be a connected reductive algebraic group. We develop a Gröbner 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 using Cartan decomposition. Our work partly builds on the previous work of Vogiannou on spherical tropicalization and in some ways is complementary.

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ER -

GRÖBNER THEORY AND TROPICAL GEOMETRY ON SPHERICAL VARIETIES

Abstract

Bibliographical note

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ASJC Scopus subject areas

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