Related papers: Positivity for partial tropical flag varieties
We classify the invariant prime ideals of a quantum partial flag variety under the action of the related maximal torus. As a result we construct a bijection between them and the torus orbits of symplectic leaves of the standard Poisson…
In this manuscript we study the subdivisions of the permutahedron $\Pi_n$ into two subpolytopes corresponding to flags of positroids, which are in particular flags of lattice path matroids (LPFMs). A subpolytope $P_{[u,v]}$ of $\Pi_n$ is a…
We establish a natural and geometric 1-1 correspondence between projective toric varieties of dimension $n$ and horofunction compactifications of $\mathbb{R}^n$ with respect to rational polyhedral norms. For this purpose, we explain a…
Tropical ideals, introduced in arXiv:1609.03838, define subschemes of tropical toric varieties. We prove that the top-dimensional parts of their varieties are balanced polyhedral complexes of the same dimension as the ideal. This means that…
We study a natural generalization of the noncrossing relation between pairs of elements in [n] to k-tuples in [n] that was first considered by Petersen, Pylyavskyy, Speyer (2010). We give an alternative approach to their result that the…
We show that the tropical projective Grassmannian of planes is homeomorphic to a closed subset of the analytic Grassmannian in Berkovich's sense by constructing a continuous section to the tropicalization map. Our main tool is an explicit…
For a variety with a Whitney stratification by affine spaces, we study categories of motivic sheaves which are constant mixed Tate along the strata. We are particularly interested in those cases where the category of mixed Tate motives over…
We show that the number of combinatorial types of clusters of type $D_4$ modulo reflection-rotation is exactly equal to the number of combinatorial types of tropical planes in $\mathbb{TP}^5$. This follows from a result of Sturmfels and…
Tropical varieties are polyhedral shadows of classical varieties. The purpose of these expository notes is to explain the origin of this polyhedral complex structure from the perspective of Gr\"obner bases. To appear in the proceedings of…
We give a complete classification of anisotropic projective homogeneous varieties of dimension less than 6 up to motivic isomorphism. We give several criteria for anisotropic flag varieties of type A_n to have isomorphic motives.
Our concern in this paper is the dimension and inclusion relations of Schubert varieties in twisted partial affine flag varieties. In the end we apply our results to some local models of certain Schubert varieties.
A Kazhdan-Lusztig variety is the intersection of a locally-closed Schubert cell with an opposite Schubert variety in a flag variety. We present a linear parametrization of the Schubert cells in the affine type A flag variety via…
The goal of this paper is to study the link between the topology of the degenerate flag varieties and combinatorics of the Dellac configurations. We define three new classes of algebraic varieties closely related to the degenerate flag…
We study two-step flag positroids $(P_1, P_2)$, where $P_1$ is a quotient of $P_{2}$. We provide a complete characterization of all two-step flag positroids that contain a uniform matroid, extending and completing a partial result by…
Valuated term orders are studied for the purposes of Gr\"{o}bner theory over fields with valuation. The points of a usual tropical variety correspond to certain valuated terms preorders. Generalizing both of these, the set of all…
The subject of the present paper is phase tropicalization, which was used crucially in the context of Mikhalkin's correspondence theorem for curve counting in the complex coefficient case. The subject can be traced back to Viro's…
Levi subgroup actions on Schubert varieties are studied. In the case of partial flag varieties, the horospherical actions are determined. This leads to a characterization of the toroidal and horospherical partial flag varieties with Picard…
Let G be a semisimple simply connected group of simply laced type over C. We show that the flag manifold of G has a version defined over the "tropical" semifield Z on which the monoid G(Z) associated to G and the semifield Z acts.
We extend tropicalization and tropical compactification of subvarieties of algebraic tori to subvarieties of spherical homogeneous spaces. Given a tropical compactification of a subvariety, we show that the support of the colored fan of the…
Double Bruhat cells in a connected complex semisimple Lie group $G$ emerged as a crucial concept in the work of S. Fomin and A. Zelevinsky on total positivity and cluster algebras. These cells are special instances of a broader class of…