Related papers: Ample Vector Bundles and Branched Coverings, II
We study vector bundles on curves with rational tails and their smoothings and give a sufficient condition for the general fibre to be balanced.
Vector bundle cohomology represents a key ingredient for string phenomenology, being associated with the massless spectrum arising in string compactifications on smooth compact manifolds. Although standard algorithmic techniques exist for…
We use a generalization of Horrocks monads for arithmetic Cohen-Macaulay (ACM) varieties to establish a cohomological characterization of linear and Steiner bundles over projective spaces and quadric hypersurfaces. We also study resolutions…
We examine the topological characteristic cohomology classes of complexified vector bundles. In particular, all the classes coming from the real vector bundles underlying the complexification are determined.
We study the moduli stacks of real vector bundles of fixed rank and degree on a type I real algebraic curve and determine its mod 2 cohomology algebra in terms of characteristic classes.
The article is devoted to microbundles over topological rings. Their structure, homomorphisms, automorphisms and extensions are studied. Moreover, compactifications and inverse spectra of microbundles over topological rings are…
We study extension properties for morphisms of stacks of bundles for group algebraic spaces. Applications are a short proof of the classification of bundles on the projective line for smooth geometrically reductive groups and the existence…
We improve Ottaviani's splitting criterion for vector bundles on a quadric hypersurface and obtain the equivalent of the result by Rao, Mohan Kumar and Peterson. Then we give the classification of rank 2 bundles without "inner" cohomology…
In 1991 Campana and Peternell proposed, as a natural algebro-geometric extension of Mori's characterization of the projective space, the problem of classifying the complex projective Fano manifolds whose tangent bundle is nef, conjecturing…
In this work we study the connection between the existence of finite dihedral covers of the projective plane ramified along an algebraic curve C, infinite dihedral covers, and pencils of curves containing C.
Let X be a smooth complex projective variety of dimension d. It is classical that ample line bundles on X satisfy many beautiful geometric, cohomological, and numerical properties that render their behavior particularly tractable. By…
In this paper, we study the structure of projective space bundles whose relative anti-canonical line bundle is nef. As an application, we get a characterization of abelian varieties up to finite etale covering.
Applying concepts and tools from classical tangent bundle geometry and using the apparatus of the calculus along the tangent bundle projection ('pull-back formalism'), first we enrich the known lists of the characterizations of affine…
In the mid 70's, Hartshorne conjectured that, for all n > 7, any rank 2 vector bundles on P^n is a direct sum of line bundles. This conjecture remains still open. In this paper, we construct indecomposable rank two vector bundles on a large…
In this paper, we give some results on the birational geometry of varieties of Fano type and boundedness problems in positive characteristic, including a result ensuring that boundedness is invariant under normalizations, a canonical bundle…
We study the complex-analytic geometry of semi-positive holomorphic line bundles on compact K\"ahler manifolds. In one of our main results, for a $\mathbb{Q}$-effective line bundle satisfying a natural torsion-type assumption, we show the…
We discuss algebraic vector bundles on smooth k-schemes X contractible from the standpoint of A^1-homotopy theory; when k = C, the smooth manifolds X(C) are contractible as topological spaces. The integral algebraic K-theory and integral…
Let X be a Fano threefold, and let S be a K3 surface in X . Any moduli space M of simple vector bundles on S carries a holomorphic symplectic structure. Following an idea of Tyurin, we show that in some cases, those vector bundles which…
We generalize Bertram's work on rank two vector bundles to an irreducible projective nodal curve C. We use extensions of a line bundle L by O_C and the associated `forgetful' map to study a compactification of the moduli space of…
Stratifications and iterative differential equations are analogues in positive characteristic of complex linear differential equations. There are few explicit examples of stratifications. The main goal of this paper is to construct…