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

Christopher Manon, Jihyeon Jessie Yang

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)199-231
Number of pages33
JournalCanadian Journal of Mathematics
Volume74
Issue number1
DOIs
StatePublished - Feb 12 2022

Bibliographical note

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

Keywords

  • Compactification
  • Newton-Okounkov body
  • Tropical geometry

ASJC Scopus subject areas

  • General Mathematics

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