Related papers: On higher rank globally generated vector bundles o…

In this article, we investigate the stability of syzygy bundles corresponding to ample and globally generated vector bundles on smooth irreducible projective surfaces.

We associate to each toric vector bundle on a toric variety X(Delta) a "branched cover" of the fan Delta together with a piecewise-linear function on the branched cover. This construction generalizes the usual correspondence between toric…

This paper introduces $\infty$- and $n$-fold vector bundles as special functors from the $\infty$- and $n$-cube categories to the category of smooth manifolds. We study the cores and "n-pullbacks" of $n$-fold vector bundles and we prove…

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 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…

Rank 2 indecomposable arithmetically Cohen-Macaulay bundles E on a nonsingular cubic surface X in P^3 are classified, by means of the possible forms taken by the minimal graded free resolution of E over P^3. The admissible values of the…

Clifford indices of vector bundles on algebraic curves were introduced in a previous paper of the authors. In this paper we study bundles of rank 2 which compute these Clifford indices. This is of particular interest in the light of…

We study the problem of when a topological vector bundle on a smooth complex affine variety admits an algebraic structure. We prove that all rank $2$ topological complex vector bundles on smooth affine quadrics of dimension $11$ over the…

We review the notions of symplectic and orthogonal vector bundles over curves, and the connection between principal parts and extensions of vector bundles. We give a criterion for a certain extension of rank 2n to be symplectic or…

We give a partial positive answer to a conjecture of Tyurin (\cite {Tyu}). Indeed we prove that on a general quintic hypersurface of $\Pj^4$ every arithmetically Cohen--Macaulay rank 2 vector bundle is infinitesimally rigid.

Let $X$ be a smooth projective variety of dimension $5$ and $L$ be an ample line bundle on $X$ such that $L^5>7^5$ and $L^d\cdot Z\geq 7^d$ for any subvariety $Z$ of dimension $1\leq d\leq 4$. We show that $\mathcal{O}_X(K_X+L)$ is globally…

Let $G$ be an algebraic group and let $X$ be a smooth $G$-variety with two orbits: an open orbit and a a closed orbit of codimension $1$. We give an algebraic description of the category of $G$-equivariant vector bundles on $X$ under a mild…

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…

Let $f:X\rightarrow Y$ be a generically smooth morphism between irreducible smooth projective curves over an algebraically closed field of arbitrary characteristic. We prove that the vector bundle $((f_*{\mathcal O}_X)/{\mathcal O}_Y)^*$ is…

We determine the Chern classes of globally generated rank two vector bundles on P^2.

Let X be a smooth projective curve of genus g bigger then 2. For any vector bundle E on X let M_k(E) be the scheme of all rank k subbundles of E with maximal degree. For every integers r, k and x with 0<k<r, x positive and either x less…

Let $S$ be a ruled surface inside a smooth threefold $W$ and let $E$ be a vector bundle on a formal neighborhood of $S.$ We find minimal conditions under which the local moduli space of $E$ is finite dimensional and smooth. Moreover, we…

We study smooth quadric surfaces in the Pfaffian hypersurface in $\mathbb{P}^{14}$ parameterising $6 \times 6$ skew-symmetric matrices of rank at most 4, not intersecting the Grassmannian $\mathbb{G}(1,5)$. Such surfaces correspond to…

Let W be the germ of a smooth complex surface around an exceptional curve and let E be a rank 2 vector bundle on W. We study the cohomological properties of a finite sequence $E_i, 1 \leq i \leq t$ of rank 2 vector bundles canonically…

In this work we deal with vector bundles of rank two on a Fano manifold $X$ with $b_2=b_4=1$. We study the nef and pseudoeffective cones of the corresponding projectivizations and how these cones are related to the decomposability of the…