Related papers: A projection formula for the ind-Grassmannian

I conjecture that index formulas for $K$-theory classes on the moduli of holomorphic $G$-bundles over a compact Riemann surface $\Sigma$ are controlled, in a precise way, by Frobenius algebra deformations of the Verlinde algebra of $G$. The…

Let $\mathcal{O}(U)$ denote the algebra of holomorphic functions on an open subset $U\subset\mathbb{C}^n$ and $Z\subset\mathcal{O}(U)$ its finite-dimensional vector subspace. By the theory of least space of de Boor and Ron, there exists a…

In the example of complex grassmannians, we demonstrate various techniques available for computing genus-0 K-theoretic GW-invariants of flag manifolds and more general quiver varieties. In particular, we address explicit reconstruction of…

We define several versions of a class of varieties $X_{\mathfrak{g}}$ attached to a complex reductive Lie algebra $\mathfrak{g}$, generalizing the Hilbert scheme of points on the plane. These include trigonometric and elliptic versions…

Let $X$ be a projective toric variety of dimension $n$ and let $L$ be a ample line bundle on $X$. For $k \geq 0$, it is in general difficult to determine whether $L^{\otimes k}$ is very ample and whether it additionally gives a projectively…

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…

For a reductive group $G$, Harder-Narasimhan theory gives a structure theorem for principal $G$ bundles on a smooth projective curve $C$. A bundle is either semistable, or it admits a canonical parabolic reduction whose associated Levi…

An index theory for projective families of elliptic pseudodifferential operators is developed when the twisting, i.e. Dixmier-Douady, class is decomposable. One of the features of this special case is that the corresponding Azumaya bundle…

Let $\Theta=(\theta_{jk})_{n\times n}$ be a real skew-symmetric $n\times n$ matrix for $n\geq 2$. Under some mild non-integrality conditions on $\Theta,$ we construct Rieffel-type projections as higher dimensional Bott classes in the…

Using symmetrized Grassmannians we give an algebraic geometric presentation, in the level of classifying spaces, of the Chern character and its relation to Chern classes. This allows one to define, for any projective variety $X$, a Chern…

A metric introduced on a projective space yields a homogeneous metric space known as a Cayley-Klein geometry. This construction is applicable not only to Euclidean and non-Euclidean spaces but also to kinematic spaces (space-times). A…

Given a complex vector space $V$ of finite dimension, its Grassmannian variety parametrizes all subspaces of $V$ of a given dimension. Similarly, if a finite group $G$ acts on $V$, its invariant Grassmannian parametrizes all the…

Let $R$ be an algebra over a ring $\Bbbk$, $T$ an $R$-algebra, $M$ a finitely generated projective $R$-module, and $N$ a $T$-module. Let $G$ be a linearly reductive group scheme over $\Bbbk$ equipped with a representation…

We establish a formula for the classes of certain tori in the Grothendieck ring of varieties, in terms of its lambda-structure. More explicitly, we will see that if L* is the torus of invertible elements in the n-dimensional separable…

Let G be a linear algebraic group defined over a field k. We prove that, under mild assumptions on k and G, there exists a finite k-subgroup S of G such that the natural map H^1(K, S) -> H^1(K, G) is surjective for every field extension…

Let $\mathfrak{X}$ be a class of finite groups closed under subgroups, homomorphic images, and extensions. We study the question which goes back to the lectures of H. Wielandt in 1963-64: For a given $\mathfrak{X}$-subgroup $K$ and maximal…

Let $V$ be an $n$-dimensional left vector space over a division ring $R$ and $n\ge 3$. Denote by ${\mathcal G}_{k}$ the Grassmann space of $k$-dimensional subspaces of $V$ and put ${\mathfrak G}_{k}$ for the set of all pairs $(S,U)\in…

In this article, we study the Heller relative $K_{0}$ group of the map $\mathbb{P}_{X}^{r} \to \mathbb{P}_{S}^{r},$ where $X$ and $S$ are quasi-projective schemes over a commutative ring. More precisely, we prove that the projective bundle…

Let $SU_X(n,L)$ be the moduli space of rank n semistable vector bundles with fixed determinant L on a smooth projective genus g curve X. Let $SU_X^s(n,L)$ denote the open subset parametrizing stable bundles. We show that if g>3 and n > 1,…

The main goal of the paper is to provide a quantitative lower bound greater than $1$ for the relative projection constant $\lambda(Y, X)$, where $X$ is a subspace of $\ell_{2p}^m$ space and $Y \subset X$ is an arbitrary hyperplane. As a…