Related papers: Limites de fibres vectoriels dans ${\bf M}_{\mathb…

In our previous papers [Far East Journal of Mathematical Sciences, 35 (2009), 211-223] and [International Journal of Pure and Applied Mathematics, 60 (2010), 15-24] we have developed the theory of Weil prolongation, Weil exponentiability…

Let E be a stable rank 2 vector bundle on a smooth quadric threefold Q in the projective 4-space P. We show that the hyperplanes H in P for which the restriction of E to the hyperplane section of Q by H is not stable form, in general, a…

Let Y be a subvariety of a smooth projective variety X, and V a vector bundle on X. Given that the restriction of V to Y splits into a direct sum of line bundles, we ask whether V splits on X. I answer this question in affirmative if holds:…

We generalize Horrocks' criterion for the splitting of vector bundles on projective space. We establish an analogous splitting criterion for vector bundles on a class of smooth complex projective varieties of dimension at least four, over…

Clifford indices for semistable vector bundles on a smooth projective curve of genus at least 4 were defined in previous papers of the authors. In the present paper, we establish lower bounds for the Clifford indices for rank 3 bundles. As…

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…

We study smooth bundles over surfaces with highly connected almost parallelizable fiber $M$ of even dimension, providing necessary conditions for a manifold to be bordant to the total space of such a bundle and showing that, in most cases,…

We study different notions of slope of a vector bundle over a smooth projective curve with respect to ampleness and affineness in order to apply this to tight closure problems. This method gives new degree estimates from above and from…

Let X be a very general Debarre-Voisin fourfold. In this article, we prove that all the Schur functors of the restriction of the quotient bundle of Gr(6,10) to X are modular and polystable vector bundles. We also show that such bundles are…

We classify nef vector bundles on a smooth hyperquadric of dimension $\geq 4$ with first Chern class two over an algebraically closed field of characteristic zero.

We classify nef vector bundles on a smooth quadric surface with first Chern class $(2,2)$ over an algebraically closed field of characteristic zero.

It is easy to imagine that a subvariety of a vector bundle, whose intersection with every fibre is a vector subspace of constant dimension, must necessarily be a sub-bundle. We give two examples to show that this is not true, and several…

A degree $d$ genus $g$ cover of the complex projective line by a smooth irreducible curve $C$ yields a vector bundle on the projective line by pushforward of the structure sheaf. We classify the bundles that arise this way when $d = 5$.…

Let $E$ be an indecomposable rank two vector bundle on the projective space $\PP^n, n \ge 3$, over an algebraically closed field of characteristic zero. It is well known that $E$ is arithmetically Buchsbaum if and only if $n=3$ and $E$ is a…

Let $R$ be an excellent Henselian discrete valuation ring with algebraically closed residue field $k$ of any characteristic. Fix integers $r,d$ with $r\ge 2$. Let $X_R$ be a regular fibred surface over Spec($R$) with special fibre denoted…

Let $\Cal E$ be a very ample vector bundle of rank two on a smooth complex projective threefold $X$. An inequality about the third Segre class of $\Cal E$ is provided when $K_X+\det \Cal E$ is nef but not big, and when a suitable positive…

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…

We give a complete classification of globally generated vector bundles of rank 3 on a smooth quadric threefold with $c_1\leq 2$ and extend the result to arbitrary higher rank case. We also investigate the existence of globally generated…

We study the following question: Given a vector bundle on a projective variety $X$ such that the restriction of $E$ to every closed curve $C \,\subset\, X$ is ample, under what conditions $E$ is ample? We first consider the case of an…

The paper studies a rank 2 vector bundle on P1 x P3. Similarly to the Horrocks - Mumford bundle on P4 this vector bundle encodes a lot of geometric information. It is defined via the Serre construction by an abelian surface in P1 x P3. The…