Related papers: Relative Bott-Samelson varieties
Let $u\in\mathrm{End}(\mathbb{C}^n)$ be nilpotent. The variety of $u$-stable complete flags is called the Springer fiber over $u$. Its irreducible components are parameterized by a set of standard Young tableaux. The Richardson (resp.…
In this paper we introduce the notion of almost flatness for (stably) relative bundles on a pair of topological spaces and investigate basic properties of it. First, we show that almost flatness of topological and smooth sense are…
We study the coherent cohomology of generalized flag supervarieties. Our main observation is that these groups are closely related to the free resolutions of (certain generalizations of) determinantal ideals. In the case of super…
The formulation of the local BRST cohomology on infinite jet bundles and its relation and reduction to gauge covariant algebras are reviewed. As an illustration, we compute the local BRST cohomology for geodesic motion in (pseudo-)…
Given any toric subvariety $Y$ of a smooth toric variety $X$ of codimension $k$, we construct a length $k$ resolution of $\mathcal O_Y$ by line bundles on $X$. Furthermore, these line bundles can all be chosen to be direct summands of the…
The classical Brill-Noether theorems count the dimension of the family of maps from a general curve of genus g to non-degenerate curves of degree d in r-dimensional projective space. These theorems can be extended to include ramification…
Playing off against each other the real and complex structures, we elucidate the local structure of certain representation spaces in the world of Poisson geometry. Particular cases of these spaces arise as moduli spaces of semistable…
An alternative proof of bornological Verdier duality for complex manifolds, as proven initially by Prosmans & Schneiders is given, using Schneider's theory of quasi-abelian homological algebra, and the theory of residues and duality.
In this paper we study the Brill-Noether theory of sub-line bundles of a general, stable rank-two vector bundle on a curve C with general moduli. We relate this theory to the geometry of unisecant curves on smooth, non-special scrolls with…
In this article we study the cohomological and homological (due to Jannsen) Hodge conjecture for singular varieties. The motivation for studying singular varieties comes from the fact that any smooth projective variety X is birational to a…
Let $X/\mathbb{F}_{q}$ be a smooth geometrically connected variety. Inspired by work of Corlette-Simpson over $\mathbb{C}$, we formulate a conjecture that absolutely irreducible rank 2 local systems with infinite monodromy on $X$ come from…
In this article, we extend the van Hamel-Lichtenbaum duality theorem to (not necessarily smooth) proper and geometrically integral varieties defined over a $p$-adic field $k$. More precisely, we prove that for such variety $X$ there exists…
We study subvarieties of the flag variety called Hessenberg varieties, defined by certain linear conditions. These subvarieties arise naturally in applications including geometric representation theory, number theory, and numerical…
We study vector bundles over Lie groupoids, known as VB-groupoids, and their induced geometric objects over differentiable stacks. We establish a fundamental theorem that characterizes VB-Morita maps in terms of fiber and basic data, and…
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…
Most applications of the hard Lefschetz theorem related to combinatorial properties of simplicial complexes involve their $h$-vectors. In the context of positivity properties involving $h$-vectors of flag spheres, $f$-vectors with a…
Virtual braids are a combinatorial generalization of braids. We present abstract braids as equivalence classes of braid diagrams on a surface, joining two distinguished boundary components. They are identified up to isotopy, compatibility,…
A ribbon is a double structure on P^1. The geometry of a ribbon is closely related to that of a smooth curve. In this note we consider linear series on ribbons. Our main result is an explicit determinantal description for the locus…
Let X be a smooth complex algebraic variety. In this paper, we associate, to each exact n-cube of hermitian vector bundles over X, a differential form, called higher Bott Chern form, which generalizes the Bott Chern forms associated to an…
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…