Related papers: Nested fibre bundles in Bott-Samelson varieties
We consider the T-equivariant cohomology of Bott-Samelson desingularisations of Schubert varieties in the flag manifold of a connected semi-simple complex algebraic group of adjoint type with maximal torus T. We construct a combinatorially…
We construct combinatorial bases of the $T$-equivariant ($T$ is the maximal torus) cohomology $H^\bullet_T(\Sigma,k)$ of the Bott-Samelson variety $\Sigma$ under some mild restrictions on the field of coefficients $k$. This bases allow us…
Let $T$ be a maximal torus of a semisimple complex algebraic group, $\mathrm{BS}(s)$ be the Bott-Samelson variety for a sequence of simple reflections $s$ and $\mathrm{BS}(s)^T$ be the set of $T$-fixed points of $\mathrm{BS}(s)$. We prove…
Let $G$ denote an adjoint semi-simple group over an algebraically closed field and $T$ a maximal torus of $G$. Following Contou-Carr\`ere [CC], we consider the Bott-Samelson resolution of a Schubert variety as a variety of galleries in the…
This article explores the relationship between Schubert varieties and equivariant embeddings, using the framework of homogeneous fiber bundles over flag varieties. We show that the homogenous fiber bundles obtained from…
We consider all Bott-Samelson varieties ${\rm BS}(s)$ for a fixed connected semisimple complex algebraic group with maximal torus $T$ as the class of objects of some category. The class of morphisms of this category is an extension of the…
We use the toric degeneration of Bott-Samelson varieties and the description of cohomolgy of line bundles on toric varieties to deduce vanishings results for the cohomology of lines bundles on Bott-Samelson varieties.
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…
We introduce the notion of flag Bott-Samelson variety as a generalization of Bott-Samelson variety and flag variety. Using a birational morphism from an appropriate Bott-Samelson variety to a flag Bott-Samelson variety, we compute…
We introduce a method for producing congruences between Hecke eigenclasses, possibly torsion, in the coherent cohomology of automorphic vector bundles on certain good reduction Shimura varieties. The congruences are produced using some…
The aim of this paper is to describe the topological $K$-ring, in terms of generators and relations of a flag Bott manifold. We apply our results to give a presentation for the topological K-ring and hence the Grothendieck ring of algebraic…
We consider projection and lifting of labelled galleries to and from roots subsystems. Our constructions allow us to construct some topological embeddings of Bott-Samelson varieties skew equivariant with respect to the compact torus and…
In this text, We compute the equivariant cohomology of Bott-Samelson varieties. Thanks to this computation, we give a new demonstration for the formulas proved by Sarah Billey for the equivariant cohomology of Schubert varieties.
A Bott manifold is a smooth projective toric variety having an iterated $\mathbb{C} P^1$-bundle structure. A certain family of Bott manifolds is used to understand the structure of Bott--Samelson varieties (or…
Based on Morse theory for the energy functional on path spaces we develop a deformation theory for mapping spaces of spheres into orthogonal groups. This is used to show that these mapping spaces are weakly homotopy equivalent, in a stable…
We prove that the Gromov width of any Bott-Samelson variety birational to a Schubert variety and equipped with a rational K\"ahler form equals the symplectic area of a minimal curve. From this, we derive an estimate for the Seshadri…
We place the representation variety in the broader context of abelian and nonabelian cohomology. We outline the equivalent constructions of the moduli spaces of flat bundles, of smooth integrable connections, and of holomorphic integrable…
We prove that the prime torsion in the local integral intersection cohomology of Schubert varieties in the flag variety of the general linear group grows exponentially in the rank. The idea of the proof is to find a highly singular point in…
We construct a basis of the equivariant $K$-theory of Bott towers, and we describe precisely the multiplicative structure of these algebras. We deduce similar results for Bott-Samelson varieties. Thanks to the link between flag varieties…
Let $X$ be a torus manifold with locally standard action of a compact torus $T$ of half the dimension and orbit space a homology polytope. Smooth complete complex toric varieties and quasi-toric manifolds are examples of torus manifolds.…