English

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