Related papers: A classification of complex rank 3 vector bundles …

We study the vector bundles without intermediate cohomology on Fano threefolds of index two, degree d=3,4,5 and Betti number one. We obtain a complete characterization in the case of rank-two vector bundles. For arbitrary rank, we give all…

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 $d = 6$.…

Let $Y$ be a smooth projective curve of genus $g\ge 2$ and let $M_{r,d}(Y)$ be the moduli space of stable vector bundles of rank $r$ and degree $d$ on $Y$. A classical conjecture of Newstead and Ramanan states that $ c_i(M_{2,1}(Y))=0$ for…

In order to obtain existence criteria for orthogonal instanton bundles on $\mathbb{P}^n$, we provide a bijection between equivalence classes of orthogonal instanton bundles with no global sections and symmetric forms. Using such…

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…

Two definitions of the Clifford index for vector bundles on a smooth projective curve $C$ of genus $g\ge4$ were introduced in a previous paper by the authors. In another paper the authors obtained results on one of these indices for bundles…

Given a parabolic vector bundle, we construct for it a projectivization and tautological line bundle. These are analogs of the projectivization and tautological line bundle for an usual vector bundle. Using these we give a construction of…

We provide a classification of type AI topological quantum systems in dimension d=1,2,3,4 which is based on the equivariant homotopy properties of "Real" vector bundles. This allows us to produce a fine classification able to take care also…

We show that a flat principal bundle with compact connected structure group and its adjoint bundles of Lie groups have the same cohomology as the trivial bundle, which is done by proving they satisfy the condition for the Leray-Hirsch…

We consider the problem of constructing matrices of linear forms of constant rank by focusing on the associated vector bundles on projective spaces. Important examples are given by the classical Steiner bundles, as well as some special…

We describe the integral equivariant cohomology ring of a weighted projective space in terms of piecewise polynomials, and thence by generators and relations. We deduce that the ring is a perfect invariant, and prove a Chern class formula…

In the paper I introduce a new characteristic class $c(E)$ for a finite rank vector bundle $E$ on an affine scheme $S:=Spec(A)$ - the fundamental class of $E$. The class $c(E)$ is not a characteristic class in the classical sense in the…

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…

Given positive integers $r$ and $c$, let $\phi(r,c)$ denote the number of isomorphism classes of complex rank $r$ topological vector bundles on $\mathbb{CP}^{r+c}$ that are stably trivial. We compute the $p$-adic valuation of the number…

Kontsevich's characteristic classes are invariants of framed smooth fiber bundles with homology sphere fibers. It was shown by Watanabe that they can be used to distinguish smooth $S^4$-bundles that are all trivial as topological fiber…

Given a Hermitian holomorphic vector bundle over a complex manifold, consider its flag bundles with the associated universal vector bundles endowed with the induced metrics. We prove that the universal formula for the push-forward of a…

We describe the second integral cohomology group of a surface bundle as the group of Chern classes of fiberwise holomorphic complex line bundles and use this to obtain information on this group.

We construct Euler and Stiefel-Whitney classes of vector bundles with quadratic form by analyzing the intersection theory of the associated quadric bundles. We also compute the Chow rings of quadric and isotropic flag bundles. Along the…

We provide a splitting criterion for supervector bundles over the projective superspaces $\mathbb{P}^{n|m}$. More precisely, we prove that a rank $p|q$ supervector bundle on $\mathbb{P}^{n|m}$ with vanishing intermediate cohomology is…

Let $Y$ be a scheme in which 2 is invertible and let $V$ be a rank $n$ vector bundle on $Y$ endowed with a non-degenerate symmetric bilinear form $q$. The orthogonal group ${\bf O}(q)$ of the form $q$ is a group scheme over $Y$ whose…