Related papers: Nesting maps of Grassmannians

Let $k,l,m,n$ be positive integers such that $m-l\ge l>k, m-l>n-k\ge k$ and $m-l>2k^2-k-1$. Let $G_{k}(\mathbb{C}^n)$ denote the Grassmann manifold of $k$-dimensional vector subspaces of $\bc^n$. We show that any continuous map…

We pursue the analysis of nesting statistics in the $O(n)$ loop model on random maps, initiated for maps with the topology of disks and cylinders in math-ph/1605.02239, here for arbitrary topologies. For this purpose we rely on the…

Let $f:G_{n,k}\longrightarrow G_{m,l}$ be any continuous map between any two distinct complex Grassmann manifolds of the same dimension where the target is not the complex projective space. We show that, for any given $k,l$, the degree of…

In this paper we study the existence of sections of universal bundles on rational homogeneous varieties -- called nestings -- classifying them completely in the case in which the Lie algebra of the automorphism group of the variety is…

Let $C$ be a smooth projective irreducible curve of genus $g$. And let $G_{\alpha}(n,d,l)$ be the moduli space of $\alpha$ stable pairs of a vector bundle of $\rank n, \deg d$ and a subspace of $H^0(C,E)$ of $\dim = l $. We find an explicit…

Let Gr(2, E) be the Grassmann bundle of two-planes associated to a general bundle E over a curve X. We prove that an embedding of Gr(2, E) by a certain twist of the relative Pl\"ucker map is not secant defective. This yields a new and more…

Let F be a finitely generated discrete group. Given a covering map H to G of Lie groups with G either compact or complex reductive, there is an induced covering map Hom(F, H) to Hom(F, G). We show that when the fundamental group of G is…

For graphs F and G an F-matching in G is a subgraph of G consisting of pairwise vertex disjoint copies of F. The number of F-matchings in G is denoted by s(F,G). We show that for every fixed positive integer m and every fixed tree F, the…

In this paper we study the topology of the space of Riemann surfaces in a simply connected space X, S_{g,n} (X, \gamma). This is the space consisting of triples, (F_{g,n}, \phi, f), where F_{g,n} is a Riemann surface of genus g and…

Let $G_{n,k}$ denote the complex Grassmann manifold of $k$-dimensional vector subspaces of $\mathbb{C}^n$. Assume $l,k\le \lfloor n/2\rfloor$. We show that, for sufficiently large $n$, any continuous map $h:G_{n,l}\to G_{n,k}$ is rationally…

Denote by $\mathbb G(k,n)$ the Grassmannian of linear subspaces of dimension $k$ in $\mathbb P^n$. We show that if $n>m$ then every morphism $\varphi: \mathbb G(k,n) \to \mathbb G(l,m)$ is constant.

Let $\bar{M}_{0,n}(G(r,V), d)$ be the coarse moduli space of stable degree $d$ maps from $n$-pointed genus $0$ curves to a Grassmann variety $G(r,V)$. We provide a recursive method for the computation of the Hodge numbers and the Betti…

Let V, W be real algebraic varieties (that is, up to isomorphism, real algebraic sets), and let X be a subset of V. A map f from X into W is said to be regular if it can be extended to a regular map defined on some Zariski locally closed…

We define a generalization $\mathfrak{G}$ of the Grassmann algebra $G$ which is well-behaved over arbitrary commutative rings $C$, even when $2$ is not invertible. In particular, this enables us to define a notion of superalgebras that does…

Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field. Criteria are given which characterize existence of a fine or coarse moduli space classifying, up to isomorphism, the representations of $\Lambda$ with fixed…

Beauville and Laszlo give an interpretation of the affine Grassmannian for Gl_n over a field k as a moduli space of, loosely speaking, vector bundles over a projective curve together with a trivialization over the complement of a fixed…

Let M and N be closed n-dimensional manifolds, and equip N with a volume form \sigma. Let \mu be an exact n-form on M. Arnold then asked the question: When can one find a map f:;N such that f*\sigma=\mu. In 1973 Eliashberg and Gromov showed…

Here, we utilize facts about the big Chern classes discovered by M. Kapranov and independently by M. V. Nori to prove certain results about the nonexistence of certain morphisms from Grassmannian to Grassmannian in characteristic 0. In…

The Grassmannians of lines in projective N-space, G(1,N), are embedded by way of the Pl"ucker embedding in the projective space P(\bigwedge^2 C^{N+1}). Let H^l be a general l-codimensional linear subspace in this projective space. We…

This paper is dedicated to the classification of uniform vector bundles of rank $d+1$ over the Grassmannian $G(d,n)$ ($d\le n-d$) over an algebraically closed field in characteristic $0$. Specifically, we show that all uniform vector…