Related papers: Linear Degenerate Tropical Flag Varieties
We construct a family of flat semitoric degenerations for the Hibi variety of every finite distributive lattice. The irreducible components of each degeneration are the toric varieties associated with polytopes forming a regular subdivision…
We define an intersection product of tropical cycles on matroid varieties (via cutting out the diagonal) and show that it is well-behaved. In particular, this enables us to intersect cycles on moduli spaces of tropical rational marked…
In this survey, we discuss linear series on tropical curves and their relation to classical algebraic geometry, describe the main techniques of the subject, and survey some of the recent major developments in the field, with an emphasis on…
We investigate the secant dimensions and the identifiablity of flag varieties parametrizing flag of sub vector spaces of a fixed vector space. We give numerical conditions ensuring that secant varieties of flag varieties have the expected…
We introduce the concept of orientation for Lagrangian matroids represented in the flag variety of maximal isotropic subspaces of dimension N in the real vector space of dimension 2N+1. The paper continues the study started in…
We introduce quivers of valuated matroids and study their tropical parameter spaces. We define quiver Dressians, which parametrize containment of tropical linear spaces after tropical matrix multiplication, and show that tropicalizations of…
We revisit the representation theory in type $A$used previously to establish that the dissimilarity vectors of phylogenetic trees are points on the tropical Grassmannian variety. We use a different version of this construction to show that…
A flag positroid of ranks $\boldsymbol{r}:=(r_1<\dots <r_k)$ on $[n]$ is a flag matroid that can be realized by a real $r_k \times n$ matrix $A$ such that the $r_i \times r_i$ minors of $A$ involving rows $1,2,\dots,r_i$ are nonnegative for…
Tropical oriented matroids were defined by Ardila and Develin in 2007. They are a tropical analogue of classical oriented matroids in the sense that they encode the properties of the types of points in an arrangement of tropical hyperplanes…
The spinor variety is cut out by the quadratic Wick relations among the principal Pfaffians of an n x n skew-symmetric matrix. Its points correspond to n-dimensional isotropic subspaces of a 2n-dimensional vector space. In this paper we…
In this paper, we study the deformation theory of degenerate algebraic curves on singular varieties which appear as the degenerate limit of families of varieties. For this purpose, we systematically develop a new method to calculate the…
We study Dressians of matroids using the initial matroids of Dress and Wenzel. These correspond to cells in regular matroid subdivisions of matroid polytopes. An efficient algorithm for computing Dressians is presented, and its…
Given a toric degeneration (a degeneration to a toric variety), over the complex numbers, we construct a surjective continuous map from a general fiber to the special fiber of the degeneration in the classical topology. The construction is…
A classification of double flag varieties of complexity 0 and 1 is obtained. An application of this problem to decomposing tensor products of irreducible representations of semisimple Lie groups is considered.
We define a toric degeneration of an integrable system on a projective manifold, and prove the existence of a toric degeneration of the Gelfand-Cetlin system on the flag manifold of type A. As an application, we calculate the potential…
We study the $\bG_a^M$ degenerations $\Fl^a_\la$ of the type $A$ flag varieties $\Fl_\la$. We describe these degenerations explicitly as subvarieties in the products of Grassmanians. We construct cell decompositions of $\Fl^a_\la$ and show…
We study geometric and combinatorial properties of the degenerate flag varieties of type A. These varieties are acted upon by the automorphism group of a certain representation of a type A quiver, containing a maximal torus T. Using the…
We use some moment graph techniques, recently introduced by Lanini and P\"utz, to provide a combinatorial description of the smooth locus in flat linear degenerations of flag varieties, generalizing a result proved by Cerulli Irelli, Feigin…
A tropical curve \Gamma is a metric graph with possibly unbounded edges, and tropical rational functions are continuous piecewise linear functions with integer slopes. We define the complete linear system |D| of a divisor D on a tropical…
Tropical geometry gives a bound on the ranks of divisors on curves in terms of the combinatorics of the dual graph of a degeneration. We show that for a family of examples, curves realizing this bound might only exist over certain…