6 papers
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…
Poset polytopes and pipe dreams: types C and B
Ievgen Makedonskyi, Igor Makhlin
The first part of this paper concerns type C. We present new explicitly defined families of algebro-combinatorial structures of three kinds: combinatorial bases in representations,…
Regular subdivisions, bounds on initial ideals, and categorical limits
George Balla, Daniel Corey, Igor Makhlin +1
Several known constructions relate initial degenerations of projective toric varieties and Grassmannians to regular subdivisions of appropriate point configurations. We define a ge…
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…