Related papers: Exceptional linear systems on curves on Enriques s…

We complete our study of linear series on curves lying on an Enriques surface by showing that, with the exception of smooth plane quintics, there are no exceptional curves on Enriques surfaces, that is, curves for which the Clifford index…

We determine the gonality and the Clifford index for curves on a compact smooth toric surface. Moreover, it is shown that their gonality are computed by pencils on the ambient surface. From the geometrical view point, this means that the…

We study the existence of linear series on curves lying on an Enriques surface and general in their complete linear system. Using a method that works also below the Bogomolov-Reider range, we compute, in all cases, the gonality of such…

We compute the Clifford index of all curves on a K3 surface with Picard group isomorphic to U(m).

We extend the results of Pareschi on the constancy of the gonality and Clifford index of smooth curves in a complete linear system on Del Pezzo surfaces of degrees $\geq 2$ to the case of Del Pezzo surfaces of degree 1, where we explicitly…

We show that every possible value for the Clifford index and gonality of a curve of a given genus on a $K3$ surface occurs.

We use vector-bundle techniques in order to compute $\dim W^1_d(C)$ where $C$ is general and smooth in a linear system on an unnodal Enriques surface. We furthermore find new examples of smooth curves on Enriques surfaces with an infinite…

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…

The main purpose in this paper is to study exceptional vector bundles on Enriques surfaces.

Given a real curve, we study special linear systems called "very special" for which the dimension does not satisfy a Clifford type inequality. We classify all these very special linear systems when the gonality of the curve is small.

We give necessary and sufficient conditions for a big and nef line bundle L of any degree on a K3 surface or Enriques surface to be k-very ample and k-spanned. Furthermore, we give necessary and sufficient conditions for a spanned and big…

We prove new slope inequalities for relatively minimal fibred surfaces, showing an influence of the relative irregularity, of the unitary rank and of the Clifford index on the slope. The argument uses Xiao's method and a new Clifford-type…

In this paper we review the notions of gonality and Clifford index of an abstract curve. For a curve embedded in a projective space, we investigate the connection between the \ci of the curve and the \gc al properties of its \emb. In…

Green's conjecture is proved for smooth curves C lying on a rational surface S with an anticanonical pencil, under some mild hypotheses on the line bundle L defined by C. Constancy of Clifford dimension, Clifford index and gonality of…

We study the Clifford dimension of an integral curve. To do so, we extend the notion of Clifford index, allowing torsion-free sheaves on its computation. We derive results for arbitrary curves, and then focus on the monomial case. In this…

For a smooth irreducible curve $C$, its second gonality $d_2$ is defined to be the minimum integer $d$ such that $C$ admits a linear series $g_d^2$. In this paper, we compute the second gonality of a smooth aCM curve $C$ lying on a smooth…

We classify singular Enriques surfaces in characteristic two supporting a rank nine configuration of smooth rational curves. They come in one-dimensional families defined over the prime field, paralleling the situation in other…

We prove that the gonality among the smooth curves in a complete linear system on a $K3$ surface is constant except for the Donagi-Morrison example. This was proved by Ciliberto and Pareschi under the additional condition that the linear…

We establish for smooth projective real curves the equivalent of the classical Clifford inequality known for complex curves. We also study the cases when equality holds.

We show, among other things, that in most cases the gonality of a subcanonical curve in projective-three space is computable by multisecants.