5,708 research outputs found
Low Rank Vector Bundles on the Grassmannian G(1,4)
Here we define the concept of -regularity for coherent sheaves on the
Grassmannian G(1,4) as a generalization of Castelnuovo-Mumford regularity on
. In this setting we prove analogs of some classical properties. We
use our notion of -regularity in order to prove a splitting criterion for
rank 2 vector bundles with only a finite number of vanishing conditions. In the
second part we give the classification of rank 2 and rank 3 vector bundles
without "inner" cohomology (i.e. H^i_*(E)=H^i(E\otimes\Q)=0 for any
) on G(1,4) by studying the associated monads.Comment: 11 pages, no figure
A splitting criterion for vector bundles on blowing ups of the plane
Let be the blowing-up of distinct points and
a vector bundle on . Here we give a cohomological criterio which is
equivalent to with a direct sum of line bundles. We
also some cohomological characterizations of very particular rank 2 vector
bundles on .Comment: 6 pages, no figure
Weakly uniform rank two vector bundles on multiprojective spaces
Here we classify the weakly uniform rank two vector bundles on
multiprojective spaces. Moreover we show that every rank weakly uniform
vector bundle with splitting type is trivial and every
rank uniform vector bundle with splitting type , splits.Comment: 6 pages no figure
Surfaces of minimal degree of tame representation type and mutations of Cohen-Macaulay modules
We provide two examples of smooth projective surfaces of tame CM type, by
showing that any parameter space of isomorphism classes of indecomposable ACM
bundles with fixed rank and determinant on a rational quartic scroll in
projective 5-space is either a single point or a projective line. For surfaces
of minimal degree and wild CM type, we classify rigid Ulrich bundles as
Fibonacci extensions. For the rational normal scrolls S(2,3) and S(3,3), a
complete classification of rigid ACM bundles is given in terms of the action of
the braid group in three strands.Comment: This version is meant to amend two inaccurate statements appearing in
the published pape
Vector bundles on Hirzebruch surfaces whose twists by a non-ample line bundle have natural cohomology
Here we study vector bundles on the Hirzebruch surface such that
their twists by a spanned, but not ample, line bundle have natural cohomology, i.e. implies
.Comment: 7 pages, no figures, to appear on Cent. Eur. J. Mat
Horrocks Correspondence on a Quadric Surface
We extend the Horrocks correspondence between vector bundles and cohomology
modules on the projective plane to the product of two projective lines. We
introduce a set of invariants for a vector bundle on the product of two
projective lines, which includes the first cohomology module of the bundle, and
prove that there is a one to one correspondence between these sets of
invariants and isomorphism classes of vector bundles without line bundle
summands.Comment: 19 page
Horrocks Correspondence on ACM Varieties
We describe a vector bundle \sE on a smooth -dimensional ACM variety in
terms of its cohomological invariants H^i_*(\sE), , and
certain graded modules of "socle elements" built from \sE. In this way we
give a generalization of the Horrocks correspondence. We prove existence
theorems where we construct vector bundles from these invariants and uniqueness
theorems where we show that these data determine a bundle up to isomorphisms.
The cases of the quadric hypersurface in and the Veronese
surface in are considered in more detail.Comment: 18 pages, not figure
Rank two aCM bundles on the del Pezzo threefold with Picard number 3
Let k be an algebraically closed field of characteristic 0. A del Pezzo
threefold F with maximal Picard number is isomorphic to P^1xP^1xP^1, where P^1
is the projective line over k. In the present paper we completely classify
locally free sheaves of rank 2 with vanishing intermediate cohomology over such
an F. Such a classification extends similar results proved by E. Arrondo and L.
Costa regarding del Pezzo threefolds with Picard number 1.Comment: 24 pages. Some minor misprints corrected, a new lemma on rational
normal curves of degree 7 inserte
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