Related papers: Splitting of supervector bundles on projective sup…

A vector bundle with connection over a supermanifold leads naturally to a notion of parallel transport along superpaths. In this note we show that {\it every} such parallel transport along superpaths comes form a vector bundle with…

Let $M$ denote the moduli space of stable vector bundles of rank $n$ and fixed determinant of degree coprime to $n$ on a non-singular projective curve $X$ of genus $g \geq 2$. Denote by $\cU$ a universal bundle on $X \times M$. We show…

In this paper we contribute to the construction of families of arithmetically Cohen-Macaulay (aCM) indecomposable vector bundles on a wide range of polarized surfaces $(X,\Oo_X(1))$ for $\Oo_X(1)$ an ample line bundle. In many cases, we…

Let $G$ be a finite abelian group acting faithfully on ${\mathbb C}{\mathbb P}^1$ via holomorphic automorphisms. In \cite{DF2} the $G$--equivariant algebraic vector bundles on $G$--invariant affine open subsets of ${\mathbb C}{\mathbb P}^1$…

Consider $E$ a vector bundle over a smooth curve $C$. We compute the $\delta$-invariant of all ample ($\mathbb{Q}$-) line bundles on $\mathbb{P}(E)$ when $E$ is strictly Mumford semistable. We also investigate the case when one assumes that…

Grothendieck-Birkhoff Theorem states that every finite dimensional vector bundle over the projective line P1 splits as the sum of one dimensional vector bundles. This can be rephrased, in terms of orders, as stating that all maximal orders…

In this paper we extend the results of Ballico and Malaspina on regularity and splitting conditions on multiprojective spaces $\mathbb{P}^{n_1}\times\cdots\times\mathbb{P}^{n_s}$.

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…

There is a long-standing conjecture which states that every uniform algebraic vector bundle of rank $r<2n$ on the $n$-dimensional projective space $\mathbb{P}^n$ over an algebraically closed field of characteristic $0$ is homogeneous. This…

Horrocks proved in 1964 that vector bundles on $P^n$ without intermediate cohomology split as direct sum of line bundles. This result has been the starting point of a great research activity on other varieties, showing interesting…

If a characteristic class for two vector bundles over the same base space does not coincide, then the bundles are not isomorphic. We give under rather common assumptions a lower bound on the topological dimension of the set of all points in…

Given a monodromy representation $\rho$ of the projective line minus $m$ points, one can extend the resulting vector bundle with connection map canonically to a vector bundle with logarithmic connection map over all of the projective line.…

We construct an I-function of the projective bundle P(V) associated with a not necessarily split vector bundle V\to B as a Fourier transform of the S^1-equivariant J-function of the total space of V and show that it lies on the Givental…

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…

This is a survey article on recent results on vector bundles on symmetric product of non-singular projective curves.

We observe that the E-resultant of a very ample rank 2 vector bundle E on a real projective curve (with no real points) is nonnegative when restricted to the space of real sections. Moreover, we show that if E has a section vanishing at…

We study the moduli space of parabolic connections of rank two on the complex projective line $\mathbb{P}^1$ minus five points with fixed spectral data. This paper aims to compute the cohomology of the structure sheaf and a certain vector…

Let $k$ be a perfect field, and $X$ an irreducible smooth projective curve over $k$. We give a criterion for a vector bundle over $X$ to admit a logarithmic connection singular over a finite subset of $X$ with given residues, where residues…

In this article we compute the mapping class group of the total space $S(\xi)$ of the sphere bundle of a 3-dimensional real vector bundle $\xi$ over the complex projective plane $\mathbb{P}^2$ with $\langle p_1(\xi), [\mathbb{P}^2] \rangle…

Strongly $\mathbb{Z}$-graded algebras or principal circle bundles and associated line bundles or invertible bimodules over a class of generalized Weyl algebras $\mathcal{B}(p;q, 0)$ (over a ring of polynomials in one variable) are…