English

Poset polytopes and pipe dreams: toric degenerations and beyond

Algebraic Geometry 2024-03-18 v1 Combinatorics Representation Theory

Abstract

We demonstrate how pipe dreams can be applied to the theory of poset polytopes to produce toric degenerations of flag varieties. Specifically, we present such constructions for marked chain-order polytopes of Dynkin types A and C. These toric degenerations also give rise to further algebraic and geometric objects such as PBW-monomial bases and Newton--Okounkov bodies. We discuss a construction of the former in the type A case and of the latter in type C.

Keywords

Cite

@article{arxiv.2403.09959,
  title  = {Poset polytopes and pipe dreams: toric degenerations and beyond},
  author = {Ievgen Makedonskyi and Igor Makhlin},
  journal= {arXiv preprint arXiv:2403.09959},
  year   = {2024}
}

Comments

Extended abstract for FPSAC 2024