37,400 research outputs found
Coherent systems of genus 0 II: Existence results for k\ge3
In this paper we continue the investigation of coherent systems of type
(n,d,k) on the projective line which are stable with respect to some value of
the parameter \alpha. We work mainly with k<n and obtain existence results for
arbitrary k in certain cases, together with complete results for k=3. Our
methods involve the use of the "flips" which occur at critical values of the
parameter.Comment: 30 pages; minor presentational change
Lower bounds for Clifford indices in rank three
Clifford indices for semistable vector bundles on a smooth projective curve
of genus at least 4 were defined in previous papers of the authors. In the
present paper, we establish lower bounds for the Clifford indices for rank 3
bundles. As a consequence we show that, on smooth plane curves of degree at
least 10, there exist non-generated bundles of rank 3 computing one of the
Clifford indices.Comment: 11 page
Bundles computing Clifford indices on trigonal curves
In this paper, we determine bundles which compute the higher Clifford indices
for trigonal curves.Comment: final version, to appear in Archiv der Mat
Hodge polynomials and birational types of moduli spaces of coherent systems on elliptic curves
In this paper we consider moduli spaces of coherent systems on an elliptic
curve. We compute their Hodge polynomials and determine their birational types
in some cases. Moreover we prove that certain moduli spaces of coherent systems
are isomorphic. This last result uses the Fourier-Mukai transform of coherent
systems introduced by Hern\'andez Ruiperez and Tejero Prieto.Comment: Minor corrections and improvements in presentation; no changes to
mathematical content. Final version to appear in Manuscripta Mat
On Poincare bundles of vector bundles on curves
Let denote the moduli space of stable vector bundles of rank and
fixed determinant of degree coprime to on a non-singular projective curve
of genus . Denote by \cU a universal bundle on . We
show that, for , the restrictions \cU|\{x\} \times M and
\cU|\{y\} \times M are stable and non-isomorphic when considered as bundles
on .Comment: 8 page
Higher rank BN-theory for curves of genus 6
Higher rank Brill-Noether theory for genus 6 is especially interesting as,
even in the general case, some unexpected phenomena arise which are absent in
lower genus. Moreover, it is the first case for which there exist curves of
Clifford dimension greater than 1 (smooth plane quintics). In all cases, we
obtain new upper bounds for non-emptiness of Brill-Noether loci and construct
many examples which approach these upper bounds more closely than those that
are well known. Some of our examples of non-empty Brill-Noether loci have
negative Brill-Noether numbers.Comment: Final version to appear in Internat. J. Math.; some typos correcte
Further examples of stable bundles of rank 2 with 4 sections
In this paper we construct new examples of stable bundles of rank 2 of small
degree with 4 sections on a smooth irreducible curve of maximal Clifford index.
The corresponding Brill-Noether loci have negative expected dimension of
arbitrarily large absolute value
Coherent Systems on Elliptic curves
In this paper we consider coherent systems on an elliptic curve which
are stable with respect to some value of a parameter . We show that the
corresponding moduli spaces, if non-empty, are smooth and irreducible of the
expected dimenson. Moreover we give precise conditions for non-emptiness of the
moduli spaces. Finally we study the variation of the moduli spaces with
.Comment: Final version with some improvements in the presentation and an
additional referenc
Higher rank BN-thory for curves of genus 5
In this paper, we consider higher rank Brill-Noether theory for smooth curves
of genus 5, obtaining new upper bounds for non-emptiness of Brill-Noether loci
and many new examples.Comment: Final version; It is published (online) in Rev. Mat. Complut. DOI
10.1007/s13163-016-0203-
Clifford indices for vector bundles on curves
For smooth projective curves the Clifford index is an important invariant
which provides a bound for the dimension of the space of sections of a line
bundle. This is the first step in distinguishing curves of the same genus. In
this paper we generalise this to introduce Clifford indices for semistable
vector bundles on curves. We study these invariants, giving some basic
properties and carrying out some computations for small ranks and for general
and some special curves. For curves whose classical Clifford index is two, we
compute all values of our new Clifford indices.Comment: Final vesrion to appear in: Alexander Schmitt (Ed.) Affine Flag
Manifolds and Principal Bundles. Birkhauser, Trends in Mathematic
- …