Related papers: Schubert Quiver Grassmannians
We construct torus equivariant desingularizations of quiver Grassmannians for arbitrary nilpotent representations of an equioriented cycle quiver. We apply this to the computation of their torus equivariant cohomology.
We consider the loci of invertible linear maps $f : \mathbb{C}^n \to {(\mathbb{C}^n)}^*$ together with pairs of flags $(E_\bullet, F_\bullet)$ in $\mathbb{C}^n$ such that the various restrictions $f : F_j \to E_i^*$ have specified ranks.…
The parabolic Kazhdan-Lusztig polynomials for Grassmannians can be computed by counting Dyck partitions. We "lift" this combinatorial formula to the corresponding category of singular Soergel bimodules to obtain bases of the Hom spaces…
We give a conjectural formula for sheaves supported on (irreducible) conormal varieties inside the cotangent bundle of the Grassmannian, such that their equivariant $K$-class is given by the partition function of an integrable loop model,…
We define the grove polynomials, a set-valued extension of forest polynomials. We show that they are $K$-theoretically dual to the quasisymmetric Schubert cells which pave the quasisymmetric flag variety, in the same way that Grothendieck…
Local models of Shimura varieties in type A can be realized inside products of Grassmannians via certain linear algebraic conditions. Laumon suggested a generalization which can be identified with a family over a line whose general fibers…
The Euler characteristic of a very affine variety encodes the algebraic complexity of solving likelihood (or scattering) equations on this variety. We study this quantity for the Grassmannian with $d$ hyperplane sections removed. We provide…
In this note, we give Gysin formulas for partial flag bundles for the classical groups. We then give Gysin formulas for Schubert varieties in Grassmann bundles, including isotropic ones. All these formulas are proved in a rather uniform way…
For a given irreducible projective variety $X$, the closure of the set of all hyperplanes containing tangents to $X$ is the projectively dual variety $X^{\vee}$. We study the singular locus of projectively dual varieties of certain…
We give an explicit natural identification between the quiver coefficients of Buch and Fulton, decomposition coefficients for Schubert polynomials, and the Schubert structure constants for flag manifolds. This is also achieved in K-theory…
Let X be an algebraic variety with an action of an algebraic group G. Suppose X has a full exceptional collection of sheaves, and these sheaves are invariant under the action of the group. We construct a semiorthogonal decomposition of…
This paper generalizes the results of the paper \cite{mi3} to the case of the general $\mathfrak{sl}_2$ Schubert varieties. We study the homomorphisms between different Schubert varieties, describe their geometry and the group of the line…
We study the representations of a class of non-commutative polynomial algebras truncated at degree 3, with one additional relation. We determine the irreducible components of their varieties of representations. We do this by showing that…
We use incidence relations running in two directions in order to construct a Kempf-Laksov type resolution for any Schubert variety of the complete flag manifold but also an embedded resolution for any Schubert variety in the Grassmannian.…
The claim in the title is proved.
We propose a combinatorial model for the Schubert structure constants of the complete flag manifold when one of the factors is Grassmannian.
Given a Schubert variety $\mathcal{S}$ contained in a Grassmannian $\mathbb{G}_{k}(\mathbb{C}^{l})$, we show how to obtain further information on the direct summands of the derived pushforward $R \pi_{*} \mathbb{Q}_{\tilde{\mathcal{S}}}$…
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.
The set of all artin level quotients of a polynomial algebra in n variables having specified socle degree and type admits a parameter space. It is in fact a quasiprojective variety, naturally embedded in a Grassmannian. We give a geometric…
Given any finite quiver, we consider a complete flag of vector spaces over each vertex. Consider the unipotent invariant subalgebra of the coordinate ring of the filtered quiver representation subspace. We prove that the dimension of the…