On the generation of certain bundles over P3

This paper was begun when the author was graduate student at Scuola Normale Superiore in Pisa     

On the generation of certain bundles over P n

In this paper we prove the following Theorem. Over an algebraically closed of characteristic ≠2 for anyn≥2 there exists an integera _n such that fora≥a _n andb≥≥max{(n ²+6n+11)a/3(n+3)+2/(n+3), a+3} the kernel of the generic morphism fromb O _P ⁿ (2) intoa O _P ⁿ (3) is a locally free sheaf generated by its global sections. The extends to bundles on P ⁿ an analogous result on P ³ (see [D,2.3]). The arguments are applications of basic ideas of the so-called «voie ouest» (see [EH]).     

On the rank of certain matrices

This note is an appendix to the paper “Osculating spaces and diophantine equations (with an Appendix by Pietro Corvaja and Umberto Zannier)” by M. Bolognesi and G. Pirola.     

On the Gieseker-Petri map for rank 2 vector bundles

Denote by W_n,d ^r the set of stable vector bundles of rank n and degree d with at least r+1 sections. We compute the singular locus of W_n,d ¹. We show that W_2,d ² is irreducible and reduced and we characterize the singular locus of W_n,d ². Partially supported by N.S.F. Grant No. DMS9100891     

On the classification of complex vector bundles of stable rank

One describes, using a detailed analysis of Atiyah-Hirzebruch spectral sequence, the tuples of cohomology classes on a compact, complex manifold, corresponding to the Chern classes of a complex vector bundle of stable rank. This classification becomes more effective on generalized flag manifolds, where the Lie algebra formalism and concrete integrability conditions describe in constructive terms the Chern classes of a vector bundle. Since deceased.     

Vanishings for the cohomology of certain families of stable rank two vector bundles onP 3

Sunto Si analizzano delle condizioni per l'annullamento della coomologia di fibrati stabili di rango 2su P ³.Dopo i primi risultati di annullamento dovuti principalmente ad Hartshorne, Chang congetturò che alcune disuguaglianze sulle, classi di Chern fossero sufficienti per l'annullamento del primo gruppo di coomologia. La congettura finora è provata solo in alcuni casi particolari. Nel lavoro si dimostra la congettura in molti altri casi. In particolare si completano alcuni risultati recenti dovuti ad Ellia affrontando il caso in cui la prima classe di Chern è dispari.     

On higher order geometry on anchored vector bundles

Some geometric objects of higher order concerning extensions, semi-sprays, connections and Lagrange metrics are constructed using an anchored vector bundle. The paper was partially supported by a 2005 MEC-CNCSIS grant.     

On stable and ample vector bundles of rank 2 on curves

Ohne Zusammenfassung     

On the intersection theory of the moduli space of rank two bundles

We give an algebro-geometric derivation of the known intersection theory on the moduli space of stable rank 2 bundles of odd degree over a smooth curve of genus g. We lift the computation from the moduli space to a Quot scheme, where we obtain the intersections via equivariant localization with respect to a natural torus action.     

On integrability of certain rank 2 sub-Riemannian structures

We discuss rank 2 sub-Riemannian structures on low-dimensional manifolds and prove that some of these structures in dimensions 6, 7 and 8 have a maximal amount of symmetry but no integrals polynomial in momenta of low degrees, except for those coming from the Killing vector fields and the Hamiltonian, thus indicating nonintegrability of the corresponding geodesic flows.     

Degenerating families of rank two bundles

We construct families of rank two bundles on , in characteristic two, where for , is a sum of line bundles, and is non-split. We construct families of rank two bundles on , in characteristic , where for , is a sum of line bundles, and is non-split.

     

Stratified-algebraic vector bundles of small rank

We investigate vector bundles on real algebraic varieties. Our goal is to construct rank 2 real and complex stratified-algebraic vector bundles with prescribed Stiefel–Whitney and Chern classes, respectively. We obtain a partial solution of this problem and present two applications.