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 $M$ denote the moduli space of stable vector bundles of rank $n$ and fixed determinant of degree coprime to $n$ on a non-singular projective curve $X$ of genus $g \geq 2$. Denote by \cU a universal bundle on $X \times M$. We show that, for $x,y \in X, x \neq y$, the restrictions \cU|\{x\} \times M and \cU|\{y\} \times M are stable and non-isomorphic when considered as bundles on $X$.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 $(E,V)$ on an elliptic curve which are stable with respect to some value of a parameter $\alpha$. 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 $\alpha$.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