Related papers: Vector bundles on algebraic varieties
We study VB-groupoids and VB-algebroids, which are vector bundles in the realm of Lie groupoids and Lie algebroids. Through a suitable reformulation of their definitions, we elucidate the Lie theory relating these objects, i.e., their…
This is a survey article on recent results on vector bundles on symmetric product of non-singular projective curves.
We study flat vector bundles over complex parallelizable manifolds.
This paper is based on my talk at ICM on recent progress in a number of classical problems of linear algebra and representation theory, based on new approach, originated from geometry of stable bundles and geometric invariant theory.
We introduce two $K$-theories, one for vector bundles whose fibers are modules of vertex operator algebras, another for vector bundles whose fibers are modules of associative algebras. We verify the cohomological properties of these…
We give a concrete description of the category of G-equivariant vector bundles on certain affine G-varieties (where G is a reductive linear algebraic group over an algebraically closed field of characteristic 0) in terms of linear algebra…
We show that the Atiyah-Hirzebruch K-theory of spaces admits a canonical generalization for stratified spaces. For this we study algebraic constructions on stratified vector bundles. In particular the tangent bundle of a stratified manifold…
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…
We investigate the analog of holomorphic vector bundles in the context of Sasakian manifolds.
This is an expository article on the theory of algebraic stacks. After introducing the general theory, we concentrate in the example of the moduli stack of vector budles, giving a detailed comparison with the moduli scheme obtained via…
This survey presents some recent results of G.-M.Greuel and the author on vector bundles over algebraic curves and on Cohen-Macaulay modules over surface singularities. It is mainly devoted to the classification problems, especially to the…
Among recently introduced new notions in real algebraic geometry is that of regulous functions. Such functions form a foundation for the development of regulous geometry. Several interesting results on regulous varieties and regulous…
We describe categories of equivariant vector bundles on certain toroidal spherical varieties in linear algebra terms: vector spaces equipped with filtrations, group and Lie algebra actions, and linear maps preserving these structures.
We investigate stratified-algebraic vector bundles on a real algebraic variety X. A stratification of X is a finite collection of pairwise disjoint, Zariski locally closed subvarieties whose union is X. A topological vector bundle on X is…
In the holomorphic or algebraic setting we consider a vector bundle E on a smooth subvariety X in a smooth variety Y over a field of characteristic zero. Assuming E extends to the l-th neighborhood of X in Y, we study cohomological…
This paper gives an overview of the main results of Brill-Noether Theory for vector bundles on algebraic curves.
We construct examples of non-isomorphic algebraic vector bundles on the punctured affine space with isomorphic pullbacks to the smooth quadric.
Let V be a smooth variety defined over the real numbers. Every algebraic vector bundle on V induces a complex vector bundle on the underlying topological space V(C), and the involution coming from complex conjugation makes it a Real vector…
The double point relation defines a natural theory of algebraic cobordism for bundles on varieties. We construct a simple basis (over the rationals) of the corresponding cobordism groups over Spec(C) for all dimensions of varieties and…
This paper establishes some hidden connections between the theory of generalized algebraic multiplicities, the intersection index of algebraic varieties, and the notion of orientability of vector bundles. The novel approach adopted in it…