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

2018/06/18 by Christopher Manon, Manon, Christopher, Jihyeon Jessie Yang +1
Computer Science · Mathematics · #14M15 #14M25 #14T05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1806.06817

openalex publication_date 2018/06/18 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We construct a family of compactifications of the affine cone of the\nGrassmannian variety of 2-planes. We show that both the tropical variety of the\nPl "ucker ideal and familiar valuations associated to the construction of\nNewton-Okounkov bodies for the Grassmannian variety can be recovered from these\ncompactifications. In this way, we unite various perspectives for constructing\ntoric degenerations of flag varieties.\n

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