781 research outputs found
Cohomological characterization of vector bundles on multiprojective spaces
We show that Horrock's criterion for the splitting of vector bundles on
\PP^n can be extended to vector bundles on multiprojective spaces and to
smooth projective varieties with the weak CM property (see Definition 3.11). As
a main tool we use the theory of -blocks and Beilinson's type spectral
sequences. Cohomological characterizations of vector bundles are also showed
Geometric collections and Castelnuovo-Mumford Regularity
The paper begins by overviewing the basic facts on geometric exceptional
collections. Then, we derive, for any coherent sheaf \cF on a smooth
projective variety with a geometric collection, two spectral sequences: the
first one abuts to \cF and the second one to its cohomology. The main goal of
the paper is to generalize Castelnuovo-Mumford regularity for coherent sheaves
on projective spaces to coherent sheaves on smooth projective varieties
with a geometric collection . We define the notion of regularity of a
coherent sheaf \cF on with respect to . We show that the basic
formal properties of the Castelnuovo-Mumford regularity of coherent sheaves
over projective spaces continue to hold in this new setting and we show that in
case of coherent sheaves on \PP^n and for a suitable geometric collection of
coherent sheaves on \PP^n both notions of regularity coincide. Finally, we
carefully study the regularity of coherent sheaves on a smooth quadric
hypersurface Q_n \subset \PP^{n+1} ( odd) with respect to a suitable
geometric collection and we compare it with the Castelnuovo-Mumford regularity
of their extension by zero in \PP^{n+1}.Comment: To appear in Math. Proc. Cambridg
An efficient path planner for large mobile platforms in cluttered environments
This paper presents a one step smooth and efficient path planning algorithm for navigating a large robotic platform in known cluttered environments. The proposed strategy, based on the generation of a novel search space, relies on non-uniform density sampling of the free areas to direct the computational resources to troubled and difficult regions, such as narrow passages, leaving the larger open spaces sparsely populated. A smoothing penalty is also associated to the nodes to encourage the generation of gentle paths along the middle of the empty spaces. Collision detection is carried out off-line during the creation of the configuration space to speed up the actual search for the path, which is done on-line. Results prove that the proposed approach considerably reduces the search space in a meaningful and practical manner, improving the computational cost of generating a path optimised for fine and smooth motion. © 2006 IEEE
Brill-Noether theory for moduli spaces of sheaves on algebraic varieties
Let be a smooth projective variety of dimension and let be an
ample line bundle on . Let be the moduli space
of -stable vector bundles on of rank and Chern classes
for . We define the Brill-Noether
filtration on as and we realize
as the th determinantal variety of a morphism
of vector bundles on , provided for and . We also compute the expected
dimension of . Very surprisingly we will see that
the Brill-Noether stratification allow us to compare moduli spaces of vector
bundles on Hirzebruch surfaces stables with respect to different polarizations.
We will also study the Brill-Noether loci of the moduli space of instanton
bundles and we will see that they have the expected dimension.Comment: 19 pages. To appear Forum Mat
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