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

Producción científica: Article › revisión exhaustiva

Resumen

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.

Idioma original	English
Páginas (desde-hasta)	199-231
Número de páginas	33
Publicación	Canadian Journal of Mathematics
Volumen	74
N.º	1
DOI	https://doi.org/10.4153/S0008414X20000735
Estado	Published - feb 12 2022

Nota bibliográfica

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

Financiación

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

Financiadores	Número del financiador
National Science Foundation Arctic Social Science Program	DMS 1500966

ASJC Scopus subject areas

General Mathematics

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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 Pl{\"u}cker 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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AU - Yang, Jihyeon Jessie

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N2 - 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.

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.

KW - Compactification

KW - Newton-Okounkov body

KW - Tropical geometry

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UR - https://www.scopus.com/pages/publications/85125092278#tab=citedBy

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DO - 10.4153/S0008414X20000735

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EP - 231

JO - Canadian Journal of Mathematics

JF - Canadian Journal of Mathematics

IS - 1

ER -

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

Resumen

Nota bibliográfica

Financiación

ASJC Scopus subject areas

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