Related papers: Threefold Nature of Graded Vector Bundles

This is a review of the basic concepts of the theory of real and complex smooth vector bundles with finite rank. Besides, the concept of a tensor field is studied within the general framework of a smooth vector bundle rather than a smooth…

We classify nef vector bundles on a projective space with first Chern class three over an algebraically closed field of characteristic zero; we see, in particular, that these nef vector bundles are globally generated if the second Chern…

We introduce the concept of a higher algebroid, generalizing the notions of an algebroid and a higher tangent bundle. Our ideas are based on a description of (Lie) algebroids as vector bundle comorphisms - differential relations of a…

Let M be a closed 3-manifold and S(M) the skein module of M at some odd root of unity. Using the Frobenius morphism, we can see S(M) as the space of global sections of a coherent sheaf over the SL2 character scheme of M. We prove that when…

Modules over a vertex operator algebra V give rise to sheaves of coinvariants on moduli of stable pointed curves. If V satisfies finiteness and semi-simplicity conditions, these sheaves are vector bundles. This relies on factorization, an…

We define 2-crossed module bundle 2-gerbes related to general Lie 2-crossed modules and discuss their properties. A 2-crossed module bundle 2-gerbe over a manifold is defined in terms of a so called 2-crossed module bundle gerbe, which is a…

We introduce and examine the notion of principal $\mathbb{Z}_2^n$-bundles, i.e., principal bundles in the category of $\mathbb{Z}_2^n$-manifolds. The latter are higher graded extensions of supermanifolds in which a $\mathbb{Z}_2^n$-grading…

We present bounds for the geometric degree of the tangent bundle and the tangential variety of a smooth affine algebraic variety $V$ in terms of the geometric degree of $V$. We first analyze the case of curves, showing an explicit relation…

Usually bundle gerbes are considered as objects of a 2-groupoid, whose 1-morphisms, called stable isomorphisms, are all invertible. I introduce new 1-morphisms which include stable isomorphisms, trivializations and bundle gerbe modules.…

We show that there exists a cubic threefold defined by an invertible polynomial that, when quotiented by the maximal diagonal symmetry group, has a derived category which does not have a full exceptional collection consisting of line…

We describe the graded isomorphisms of rings of endomorphisms of graded flags over graded division algebras. As a consequence describe the isomorphism classes of upper block triangular matrix algebras (over an algebraically closed field of…

The present paper focuses on the study of the stable category of vector bundles for the weighted projective lines of weight triple. We find some important triangles in this category and use them to construct tilting objects with tubular…

It is interesting to know, how far we can generalize the notion of a group-valued cocycle keeping the property to determine a bundle. We find a generalization for pairs of cocycles and show how these generalized pairs of cocycles can still…

We identify the category of real mixed Hodge structures with the category of vector bundles with connections (not necessarily flat) on C, equivariant with respect to C^*. Here C is the complex plane considered as a 2-dimensional real…

We extend the scope of a former paper to vector bundle problems involving more than one vector bundle. As the main application, we obtain the solution of the well-known moduli problems of vector bundles associated with general quivers.

In this note we derive a formalism for describing equivariant sheaves over toric varieties. This formalism is a generalization of a correspondence due to Klyachko, which states that equivariant vector bundles on toric varieties are…

In this paper, we compare the moduli spaces of rank-3 vector bundles stable with respect to different ample divisors over rational ruled surfaces. We also discuss the irreducibility, unirationality, and rationality of these moduli spaces.

In [1] we introduced the concept of structured space, which is a topological space that locally resembles some algebraic structures. In [2] we proceeded the study of these spaces, developing two cohomology theories. The aim of this paper is…

We classify the module categories over the double (possibly twisted) of a finite group.

The quantization of vector bundles is defined. Examples are constructed for the well controlled case of equivariant vector bundles over compact coadjoint orbits. (Coadjoint orbits are symplectic spaces with a transitive, semisimple symmetry…