Related papers: Categories of vector spaces and Grassmannians

Given an arbitrary topological complex vector space $A$, a quotient vector bundle for $A$ is a quotient of a trivial vector bundle $\pi_2:A\times X\to X$ by a fiberwise linear continuous open surjection. We show that this notion subsumes…

We define functorial isomorphisms of parallel transport along etale paths for a class of vector bundles on a p-adic curve. All bundles of degree zero whose reduction is strongly semistable belong to this class. In particular, they give rise…

In this article we announce some results on compactifying moduli spaces of rank-2 vector bundles on surfaces by spaces of vector bundles on trees of surfaces. This is thought as an algebraic counterpart of the so called bubbling of vector…

We describe a variant of K-theory for spaces with involution, built from vector bundles which are sent to their negative under the involution.

A pseudo-Riemannian manifold is said to be spacelike Jordan IP if the Jordan normal form of the skew-symmetric curvature operator depends upon the point of the manifold, but not upon the particular spacelike 2-plane in the tangent bundle at…

A plane curve C defined by a homogeneous polynomial satisfying Laplace's equation appears canonically as the vanishing of the Pfaffian of a skew-symmetric matrix of linear forms. As a consequence there is a natural semi-stable rank two…

In this note we use Bott-Borel-Weil theory to compute cohomology of interesting vector bundles on sequences of Grassmanians.

Vierbeins provide a bridge between the curved space of general relativity and the flat tangent space of special relativity. Both spaces should be causal and spin. We posit intertwining the two symmetries of spacetime bundles asymmetrically;…

Tangent categories are categories equipped with a tangent functor: an endofunctor with certain natural transformations which make it behave like the tangent bundle functor on the category of smooth manifolds. They provide an abstract…

Let X be a smooth complex irreducible projective variety of dimension $n \geq 2$ and $H$ be an ample line bundle on $X$. In this paper, we construct families of $\mu_H$-stable vector bundles on $X$ having fixed determinant and rank $r$,…

Let M be a simply connected Riemannian symmetric space, with at most one flat direction. We show that every Riemannian (or unitary) vector bundle with parallel curvature over M is an associated vector bundle of a canonical principal bundle,…

If a sequence of Riemannian manifolds, $X_i$, converges in the pointed Gromov-Hausdorff sense to a limit space, $X_\infty$, and if $E_i$ are vector bundles over $X_i$ endowed with metrics of Sasaki-type with a uniform upper bound on rank,…

We prove that the Kuznetsov--Polishchuk exceptional collections on rational homogeneous spaces of the symplectic groups $\mathrm{Sp}(2n,\mathbb{C})$ are full and consist of vector bundles. To achieve this, we construct several classes of…

Given a sheaf of unital commutative and associative algebras A, first we construct the k-th Grassmann sheaf G_A(k,n) of A^n whose sections induce vector subsheaves of A^n of rank k. Next we show that every vector sheaf over a paracompact…

A vector space is commonly defined as a set that satisfies several conditions related to addition and scalar multiplication. However, for beginners, it may be hard to immediately grasp the essence of these conditions. There are probably a…

We classify equivariant topological complex vector bundles over real projective plane under a compact Lie group (not necessarily effective) action. It is shown that nonequivariant Chern classes and isotropy representations at (at most)…

In this paper we look at Grothendieck's work on classifying holomorphic bundles over the complex projective line. The paper is divided into $4$ parts. The first and second part we build up the necessary background to talk about vector…

We prove a theorem classifying the equivariant $K$-theoretic pushforwards of the product of arbitrary Schur functors applied to the tautological bundle on the moduli space of framed rank $r$ torsion-free sheaves on $\mathbb{P}^2$, and its…

We define and characterize spaces of manifold-valued generalized functions and generalized vector bundle homomorphisms in the setting of the full diffeomorphism-invariant vector-valued Colombeau algebra. Furthermore, we establish point…

We introduce tropical vector bundles, morphisms and rational sections of these bundles and define the pull-back of a tropical vector bundle and of a rational section along a morphism. Afterwards we use the bounded rational sections of a…