Geodesic
Tropical geometry and Newton–Okounkov cones for Grassmannian of planes from compactifications
Canadian journal of mathematics, Tome 74 (2022) no. 1, pp. 199-231

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DOI

We construct a family of compactifications of the affine cone of the Grassmannian variety of $2$-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.
DOI : 10.4153/S0008414X20000735
Mots-clés : Compactification, tropical geometry, Newton–Okounkov body 
Manon, Christopher; Yang, Jihyeon Jessie. Tropical geometry and Newton–Okounkov cones for Grassmannian of planes from compactifications. Canadian journal of mathematics, Tome 74 (2022) no. 1, pp. 199-231. doi: 10.4153/S0008414X20000735
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     title = {Tropical geometry and {Newton{\textendash}Okounkov} cones for {Grassmannian} of planes from compactifications},
     journal = {Canadian journal of mathematics},
     pages = {199--231},
     year = {2022},
     volume = {74},
     number = {1},
     doi = {10.4153/S0008414X20000735},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X20000735/}
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