7 papers · 1 filter
Tropical cluster varieties of type C
Igor Makhlin
We explicitly describe the tropicalization of a cluster variety of finite type C, realizing it as the space of axially symmetric phylogenetic trees. We also find all occurring sign…
Tropical cluster varieties, phylogenetic trees, and generalized associahedra
Igor Makhlin
We explicitly describe the tropicalization of a type C cluster variety by identifying it with the space of axially symmetric phylogenetic trees. We also study the signed tropicaliz…
On reduced arc spaces of toric varieties
Ilya Dumanski, Evgeny Feigin, Ievgen Makedonskyi +1
An arc space of an affine cone over a projective toric variety is known to be non-reduced in general. It was demonstrated recently that the reduced scheme structure is worth studyi…
Tropicalizing binary geometries
Shelby Cox, Igor Makhlin
The type A cluster configuration space, commonly known as , is the very affine part of the binary geometry associated with the associahedron. The tropicalization…
Chain-order polytopes: toric degenerations, Young tableaux and monomial bases
Igor Makhlin
Our first result realizes the toric variety of every marked chain-order polytope (MCOP) of the Gelfand--Tsetlin poset as an explicit Gröbner (sagbi) degeneration of the flag varie…
Poset polytopes and pipe dreams: toric degenerations and beyond
Ievgen Makedonskyi, Igor Makhlin
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 mar…