Related papers: On Schubert varieties of complexity one
We unify problems about the equivariant geometry of symmetric quiver representation varieties, in the finite type setting, with the corresponding problems for symmetric varieties $GL(n)/K$ where $K$ is an orthogonal or symplectic group. In…
We study the toric degeneration of Weyl group translated Schubert divisors of a partial flag variety of Lie type A via Gelfand-Cetlin polytopes. We propose a conjecture that Schubert varieties of appropriate dimensions intersect…
Hypertoric varieties are hyperk\"ahler analogues of toric varieties, and are constructed as abelian hyperk\"ahler quotients of a quaternionic affine space. Just as symplectic toric orbifolds are determined by labelled polytopes, orbifold…
We determine the structure of the equivariant cohomology and $K$-theory of Bott towers. By restriction, we obtain similar results for Bott-Samelson varieties. This results allow us to describe more precisely the equivariant cohomology and…
A smooth projective variety with an action of a torus admits a cell decomposition, called the Bialynicki-Birula decomposition. Singularities of the closures of these cells are not well-known. One of the examples of such closures is a…
By a $B$-regular variety, we mean a smooth projective variety over $C$ admitting an algebraic action of the upper triangular Borel subgroup $B \subset SL_2(C)$ such that the unipotent radical in $B$ has a unique fixed point. A result of M.…
In this expository paper we describe a powerful combinatorial formula and its implications in geometry, topology, and algebra. This formula first appeared in the appendix of a book by Andersen, Jantzen, and Soergel. Sara Billey discovered…
Let $G$ be a finitely presented group. A new complexity called \textit{Karoubi-Weibel complexity} or \textit{covering type}, is defined for $G$. The construction is inspired by recent work of Karoubi and Weibel \cite{KW}, initially applied…
A Schubert class is called rigid if it can only be represented by Schubert varieties. The rigid Schubert classes have been classified in Grassmannians and orthogonal Grassmannians. In this paper, we study the rigidity problem in partial…
Involution Schubert polynomials represent cohomology classes of $K$-orbit closures in the complete flag variety, where $K$ is the orthogonal or symplectic group. We show they also represent $T$-equivariant cohomology classes of subvarieties…
Let $A$ be an abelian variety over a field finitely generated over $\mathbb{Q}$. We show that the finiteness of the $\ell$-primary torsion subgroup of the higher Brauer group is a sufficient criterion for the Tate conjecture to hold.…
An irreducible algebraic variety $X$ is rigid if it admits no nontrivial action of the additive group of the ground field. We prove that the automorphism group $\text{Aut}(X)$ of a rigid affine variety contains a unique maximal torus…
Let H be a homology theory for algebraic varieties over a field k. To a complete k-variety X, one naturally attaches an ideal of the coefficient ring H(k). We show that, when X is regular, this ideal depends only on the upper Chow motive of…
A T-variety is an algebraic variety X with an effective regular action of an algebraic torus T. Altmann and Hausen gave a combinatorial description of an affine T-variety X by means of polyhedral divisors. In this paper we compute the…
A one parameter set of noncommutative complex algebras is given. These may be considered deformation quantisation algebras. The commutative limit of these algebras correspond to the algebra of polynomial functions over a manifold or…
Let $X$ be a 3-dimensional affine variety with a faithful action of a 2-dimensional torus $T$. Then the space of first order infinitesimal deformations $T^1(X)$ is graded by the characters of $T$, and the zeroth graded component $T^1(X)_0$…
We study from the perspective of Borel complexity theory the classification problem for multiplier algebras associated with operator algebraic varieties. These algebras are precisely the multiplier algebras of irreducible complete…
Let X be a smooth complete toric variety. We describe the Altmann-Ilten-Vollmert equivariant deformations of toric varieties in the language of Cox rings. More precisely we construct one parameters families of deformations of X, such that…
We describe the torus-equivariant cohomology of weighted partial flag orbifolds ${\mathrm{w}}\Sigma$ of type $A$. We establish counterparts of several results known for the partial flag variety that collectively constitute what we refer to…
We provide a method for gluing (small) resolutions of singularities of Schubert varieties \(X_w\). An explicit isomorphism of \(X_w\) with an (iterated) bundle is constructed when \(w\) has an (iterated) BP decomposition. Combined with the…