107 research outputs found
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
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
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
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
Globally generated vector bundles on a smooth quadric surface
We give the classification of globally generated vector bundles of rank
on a smooth quadric surface with in terms of the indices of the
bundles, and extend the result to arbitrary higher rank case. We also
investigate their indecomposability and give the sufficient and necessary
condition on numeric data of vector bundles for indecomposability.Comment: 23 pages; Comments welcome; Several correction
Moduli spaces of rank two aCM bundles on the Segre product of three projective lines
Let P^n be the projective space of dimension n on an algebraically closed
field of characteristic 0 and F be the image of the Segre embedding of
P^1xP^1xP^1 inside P^7. In the present paper we deal with the moduli spaces of
locally free sheaves E on F of rank 2 with h^i(F,E(t))=0 for i=1,2 and each
integer t.Comment: 22 pages. Exposition improve
Globally generated vector bundles on the Segre threefold with Picard number two
We classify globally generated vector bundles on with small first Chern class, i.e. , .
Our main method is to investigate the associated smooth curves to globally
generated vector bundles via the Hartshorne-Serre construction.Comment: 21 pages; Comments welcom
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