Tropical geometry and Newton-Okounkov cones for Grassmannian of planes from compactifications

Christopher Manon; Jihyeon Jessie Yang

doi:10.4153/S0008414X20000735

Tropical geometry and Newton-Okounkov cones for Grassmannian of planes from compactifications

Christopher Manon, Jihyeon Jessie Yang

Mathematics

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

Abstract

We construct a family of compactifications of the affine cone of the Grassmannian variety of -planes. We show that both the tropical variety of the Plücker ideal and familiar valuations associated to the construction of Newton-Okounkov bodies for the Grassmannian variety can be recovered from these compactifications. In this way, we unite various perspectives for constructing toric degenerations of flag varieties.

Original language	English
Pages (from-to)	199-231
Number of pages	33
Journal	Canadian Journal of Mathematics
Volume	74
Issue number	1
DOIs	https://doi.org/10.4153/S0008414X20000735
State	Published - Feb 12 2022

Bibliographical note

Publisher Copyright:
© 2022 Cambridge University Press. All rights reserved.

Funding

C.M. was supported by the NSF (DMS 1500966) and a Simons Collaboration Grant.

Funders	Funder number
National Science Foundation (NSF)	DMS 1500966

Keywords

Compactification
Newton-Okounkov body
Tropical geometry

ASJC Scopus subject areas

General Mathematics

Access to Document

10.4153/S0008414X20000735

Cite this

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AB - We construct a family of compactifications of the affine cone of the Grassmannian variety of -planes. We show that both the tropical variety of the Plücker ideal and familiar valuations associated to the construction of Newton-Okounkov bodies for the Grassmannian variety can be recovered from these compactifications. In this way, we unite various perspectives for constructing toric degenerations of flag varieties.

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Tropical geometry and Newton-Okounkov cones for Grassmannian of planes from compactifications

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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