Tropical geometry and Newton-Okounkov cones for Grassmannian of planes from compactifications
Algebraic Geometry
2019-01-15 v2
Abstract
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 Pl\"ucker 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.
Keywords
Cite
@article{arxiv.1806.06817,
title = {Tropical geometry and Newton-Okounkov cones for Grassmannian of planes from compactifications},
author = {Christopher Manon and Jihyeon Jessie Yang},
journal= {arXiv preprint arXiv:1806.06817},
year = {2019}
}
Comments
25 pages; we added a proof that the compactifications are Fano