Related papers: On linear series with negative Brill-Noether numbe…

Based on results on Hurwitz-Brill-Noether theory obtained by H. Larson we give a picture of the irreducible components of $W^r_d(C)$ for a general $k$-gonal curve of genus $g$. This picture starts from irreducible components of $W^r_d(C)$…

We compute the rational cohomology groups of the smooth Brill-Noether varieties $G^r_d(C)$, parametrizing linear series of degree $d$ and dimension exactly $r$ on a general curve $C$. As an application, we determine the whole intersection…

A Brill-Noether locus is a subscheme of the moduli of bundles E over a curve C defined by requiring E to have a given number of sections, or homomorphisms from another bundle. There are a number of different types, that can be treated by…

Given a curve $C$ that is a degree $k$ cover $C \to \mathbb{P}^1$ totally ramified at two points $p$ and $q$, we can seek to understand the space of degree $d$ line bundles on $C$ with prescribed ramification at $p$ and $q$. The…

In this paper, we study the Brill-Noether theory of the normalizations of singular, irreducible curves on a $K3$ surface. We introduce a {\em singular} Brill-Noether number $\rho_{sing}$ and show that if the Picard group of the K3 surface…

We investigate limit linear series on chains of elliptic curves, giving a simple proof of a conjecture of Farkas stating the existence of curves with a theta-characteristic with a given number of sections for the expected range of genera.…

We prove the irreducibility of the moduli space of rank 2 semistable torsion free sheaves (with a generic polarization and any value of c_2) on a K3 or a del Pezzo surface. In the case of a K3 surface, we need to prove a result on the…

Let $C$ be a smooth projective complex curve of genus $g \geq 2$. We investigate the Brill-Noether locus consisting of stable bundles of rank 2 and determinant $L$ of odd degree $d$ having at least $k$ independent sections. This locus…

We first prove a generalized Brill-Noether theorem for linear series with prescribed multivanishing sequences on smooth curves. We then apply this theorem to prove that spaces of limit linear series have the expected dimension for a certain…

We describe a conjectural stratification of the Brill-Noether variety for general curves of fixed genus and gonality. As evidence for this conjecture, we show that this Brill-Noether variety has at least as many irreducible components as…

We show that a general curve in an explicit class of what we call Du Val pointed curves satisfies the Brill-Noether Theorem for pointed curves. Furthermore, we prove that a generic pencil of Du Val pointed curves is disjoint from all…

Let $G$ be a finite graph of genus $g$. Let $d$ and $r$ be non-negative integers such that the Brill-Noether number is non-negative. It is known that for some $k$ sufficiently large, the $k$-th homothetic refinement $G^{(k)}$ of $G$ admits…

Let C be a Brill-Noether-Petri curve of genus g\geq 12. We prove that C lies on a polarized K3 surface, or on a limit thereof, if and only if the Gauss-Wahl map for C is not surjective. The proof is obtained by studying the validity of two…

Let C be a projective smooth curve of genus g> 1. Let E be a vector bundle of rank r on C. For each integer r'<r, associate to E the invariant s_{r'}(E)=r'deg(E)-rdeg(E') where E'is a subbundle of E of rank r' and maximal degree. For every…

Let $\mathcal{H}_{d,g,r}$ be the Hilbert scheme parametrizing smooth irreducible and non-degenerate curves of degree $d$ and genus $g$ in $\PP^r$. We denote by $\mathcal{H}^\mathcal{L}_{d,g,r}$ the union of those components of…

Given an ample line bundle L on a K3 surface S, we study the slope stability with respect to L of rank-3 Lazarsfeld-Mukai bundles associated with complete, base point free nets of type g^2_d on curves C in the linear system |L|. When d is…

We consider a general curve of fixed gonality k and genus g. We propose an estimate for the dimension of the variety $W^r_d(C)$ of special linear series on C, by solving an analogous problem in tropical geometry. Using work of Coppens and…

We show that the space of linear series of certain multi-degree (including the balanced ones) and rank $r$ on a general binary curve has the expected dimension if nonempty. This generalizes Theorem 24 of Caporaso's paper about binary curves…

We study Brill-Noether loci of three kinds of spectral curves: classical spectral curves as introduced by Hitchin, spectral curves over the projective line and double covers whose branch locus is a canonical divisor. Our techniques are…

Let U(r) be the moduli space of rank r vector bundles with trivial determinant on a smooth curve of genus 2. The map theta_r: U(r) -> |r Theta|, which associates to a general bundle its theta divisor, is generically finite. In this paper we…