Related papers: Classification of equivariant vector bundles over …

We provide a classification of type AI topological quantum systems in dimension d=1,2,3,4 which is based on the equivariant homotopy properties of "Real" vector bundles. This allows us to produce a fine classification able to take care also…

We consider a smooth Lagrangian subvariety Y in a smooth algebraic variety X with an algebraic symplectic from. For a vector bundle E on Y and a choice Oh of deformation quantization of the structure sheaf of X, we establish when E admits a…

This paper gives various methods for constructing vector bundles over elliptic curves and more generally over families of elliptic curves. We construct universal families over generalized elliptic curves via spectral cover methods and also…

In this paper, we develop several pluripotential-theoretic techniques for singular metrics on vector bundles. We first introduce the theory of non-pluripolar products on holomorphic vector bundles on complex manifolds. Then we define and…

We prove stability of rank two tautological bundles on the Hilbert square of a surface (under a mild positivity condition) and compute their Chern classes.

We classify irreducible equivariant Ulrich vector bundles on isotropic Grassmannians.

A family of holomorphic vector bundles is constructed on a complex manifold $X$. The space of the holomorphic sections of these bundles are calculated in certain cases. As an application, if $X$ is an $N$-dimensional compact K\"ahler…

For finite coverings we elucidate the interaction between transferred Chern classes and Chern classes of transferred bundles. This involves computing the ring structure for the complex oriented cohomology of various homotopy orbit spaces.…

We construct a scalar invariant of flat principal 2-bundles over 3-manifolds, with structure 2-group $\mathcal{G}$, from an involutory Hopf algebra graded by $\mathcal{G}$. Expressing $\mathcal{G}$ in terms of a crossed module $\chi$ and…

We study the problem of defining line bundles over certain non-Hausdorff spaces known as Quantum Tori, motivated by the proposed theory of Real Multiplication for real quadratic fields. We draw analogies from the theory of Line Bundles over…

A formula for the first Chern class of the Verlinde bundle over the moduli space of smooth genus g curves is given. A finite-dimensional argument is presented in rank 2 using geometric symmetries obtained from strange duality, relative…

Using the theory of quantized equivariant vector bundles over compact coadjoint orbits we determine the Chern characters of all noncommutative line bundles over the fuzzy sphere with regard to its derivation based differential calculus. The…

Let G be a finite group acting on a finite dimensional real vector space V. We denote by P(V) the projective space associated to V. In this paper we compute in a very explicit way the rank of the equivariant complex K-theory of V and P(V),…

We present a geometric model for the category of vector bundles over the weighted projective line of type (2,2,n). This model is based on the orbit space of an infinite marked strip under a specific group action. We establish a bijection…

Given two equivariant vector bundles over an algebraic GKM manifold with the same equivariant Chern classes, we show that the genus zero equivariant Gromov--Witten theory of their projective bundles are naturally isomorphic.

We present two formulas for Chern classes of the tensor product of two vector bundles. In the first formula we consider a matrix containing Chern classes of the first bundle and we take a polynomial of this matrix with Chern classes of the…

In the high-energy quantum-physics literature one finds statements such as "matrix algebras converge to the sphere". Earlier I provided a general precise setting for understanding such statements, in which the matrix algebras are viewed as…

Stable, holomorphic vector bundles are constructed on an torus fibered, non-simply connected Calabi-Yau threefold using the method of bundle extensions. Since the manifold is multiply connected, we work with equivariant bundles on the…

We give a complete classification of isomorphism classes of finitely generated projective modules, or equivalently, unitary equivalence classes of projections, over the C*-algebra $C\left( \mathbb{S}_{q}^{2n+1}\right) $ of the quantum…

Given a compact K\"ahler manifold, Geometric Invariant Theory is applied to construct analytic GIT-quotients that are local models for a classifying space of (poly)stable holomorphic vector bundles containing the coarse moduli space of…