Related papers: Equivariant vector bundles over topological toric …

The second order tangent bundle $T^{2}M$ of a smooth manifold $M$ consists of the equivalent classes of curves on $M$ that agree up to their acceleration. It is known that in the case of a finite $n$-dimensional manifold $M$, $T^{2}M$…

We define equivariant Chern classes of a toric vector bundle over a proper toric scheme over a DVR. We provide a combinatorial description of them in terms of piecewise polynomial functions on the polyhedral complex associated to the toric…

In this paper, complex vector bundles of rank $r$ over $8$-dimensional spin$^{c}$ manifolds are classified in terms of the Chern classes of the complex vector bundles and the cohomology ring of the manifolds, where $r = 3$ or $4$. As an…

Let $\mathscr{V}\mathrm{ect}_n$ be the moduli stack of vector bundles of rank $n$ on schemes. We prove that, if $E$ is a Zariski sheaf of ring spectra which is equipped with finite quasi-smooth transfers and satisfies the projective bundle…

A map Y -> P^n is determined by a line bundle quotient of (O_Y)^{n+1}. In this paper, we generalize this description to the case of maps from Y to an arbitrary smooth toric variety. The data needed to determine such a map consists of a…

We discuss topological rigidity of vector bundles with asymptotically conical (AC) total spaces of rank greater than 1 with a sufficiently connected link; our focus will mainly be on ALE (asymptotically locally Euclidean) bundles. Within…

We prove that the vector bundles at the core of the Knizhnik-Zamolodchikov and quantum constructions of braid groups representations are topologically trivial bundles. We provide partial generalizations of this result to generalized braid…

This paper investigates the cohomological property of vector bundles on biprojective space. We will give a criterion for a vector bundle to be isomorphic to the tensor product of pullbacks of exterior products of differential sheaves.

We study surjective endomorphisms of projective bundles over toric varieties, achieving three main results. First, we provide a structural theorem describing endomorphisms of projectivized split bundles over arbitrary base varieties, which…

Let $X$ be a torus manifold with locally standard action of a compact torus $T$ of half the dimension and orbit space a homology polytope. Smooth complete complex toric varieties and quasi-toric manifolds are examples of torus manifolds.…

In this paper, we resolve a conjecture of Khovanskii--Monin on the Chern classes of toric variety bundles. The main result is a formula for the total Chern class of the tangent bundle of a toric variety bundle in terms of the total Chern…

I repeat my definition for quantization of a vector bundle. For the case of Toeplitz and geometric quantization of a compact Kaehler Manifold, I give a construction for quantizing any smooth vector bundle which depends functorially on a…

In each dimension n>2 there are many projective simplicial toric varieties whose Grothendieck groups of vector bundles are at least as big as the ground field. In particular, the conjecture that the Grothendieck groups of locally trivial…

We develop a ready-to-use comprehensive theory for (super) 2-vector bundles over smooth manifolds. It is based on the bicategory of (super) algebras, bimodules, and intertwiners as a model for 2-vector spaces. We discuss symmetric monoidal…

The aim of this paper is to discuss a combinatorial characterisation of stability for toric vector bundles (or equivariant reflexive sheaves) in the terms of their parliaments of polytopes, a generalization of moment polytopes for toric…

Stratified-algebraic vector bundles on real algebraic varieties have many desirable features of algebraic vector bundles but are more flexible. We give a characterization of the compact real algebraic varieties having the following…

Starting from the data of a nonsingular complex projective toric variety, we define an associated notion of toric co-Higgs bundle. We provide a Lie-theoretic classification of these objects by studying the interaction between Klyachko's fan…

Let $M=V\setminus D$ be a smooth quasi-projective variety for some smooth projective variety $V$ and a divisor $D$ with normal crossings. Assume that $M$ is diffeomorphic to a non-compact nilmanifold $\Gamma\backslash N\times\mathbb{R}^m$.…

If $X\subset\operatorname{Gr}(2,6)$ is the Fano variety of lines of a smooth cubic fourfold, then we show that the restriction to $X$ of any Schur functor of the tautological quotient bundle is modular and slope polystable. Moreover it is…

In this paper, we give a combinatorial formula for the \v{C}ech cocycles representing the power sums of the Chern roots of a holomorphic vector bundle over a complex manifold. By an observation motivation by author's previous paper, we also…