In this paper, we describe the category of bi-equivariant vector bundles on a bi-equivariant smooth (partial) compactification of a reductive algebraic group with normal crossing boundary divisors. Our result is a generalization of the description of the category of equivariant vector bundles on toric varieties established by A. As an application, we prove splitting of equivariant vector bundle...

We study ample stable vector bundles on minimal rational surfaces. give a complete classification of those moduli spaces for which the general bundle is both and globally generated. also prove that if V any bundle, then large enough direct sum V⊕n has deformations unless there an obvious numerical reason why it cannot. Previous work in this area mostly focused rank two relied primarily classica...

In this announcement we describe categories of equivariant vector bundles on certain “spherical” varieties. Our description is in linear-algebra terms: vector spaces equipped with filtrations, group and Lie-algebra actions, and linear maps preserving these structures. The two parents of our description are i) the description of G-equivariant vector bundles on homogeneous spaces G/H as H-represe...

in this paper, we formalize the menger probabilistic normed space as a category in which its objects are the menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. so, we can easily apply the results of topological vector spaces...

We show that a triangulated motivic category admits categorical Thom isomorphisms for vector bundles with an additional structure if and only the generalized cohomology theory represented by tensor unit object classes. also stable $\mathbb{A}^1$-derived does not admit oriented and, more generally, symplectic bundles. In order to do so we compute first homology sheaves of sphere spectrum class i...