Related papers: Nonemptiness of Brill-Noether loci

Let $X$ be a non-singular projective curve of genus $g\ge2$ over an algebraically closed field of characteristic zero. Let $\mo$ denote the moduli space of stable bundles of rank $n$ and degree $d$ on $X$ and $\wn $ the Brill-Noether loci…

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…

Let C be a smooth projective complex curve of genus $g\geq2$. We investigate the Brill-Noether locus consisting of stable bundles of rank 2 and canonical determinant having at least $k$ independent sections. Using the Hecke correpondence we…

Brill-Noether loci ${\mathcal M}^r_{g,d}$ are those subsets of the moduli space ${\mathcal M}_g$ determined by the existence of a linear series of degree $d$ and dimension $r$. By looking at non-singular curves in a neighborhood of a…

Let X be a general smooth projective algebraic curve of genus g>1. We prove that the moduli space G(\alpha:n,d,k) of $\alpha $-stable coherent systems of type (n,d,k) over X is empty if k>n and the Brill-Noether number is negative.…

The interplay between algebro-geometric and combinatorial Brill-Noether theory is studied. The Brill-Noether variety of a graph shown to be non-empty if the Brill-Noether number is non-negative, as a consequence of the analogous fact for…

The symplectic Brill--Noether locus ${\mathcal S}_{2n, K}^k$ associated to a curve $C$ parametrises stable rank $2n$ bundles over $C$ with at least $k$ sections and which carry a nondegenerate skewsymmetric bilinear form with values in the…

We completely describe the Brill-Noether theory for curves in the primitive linear system on generic abelian surfaces, in the following sense: given integers $d$ and $r$, consider the variety $V^r_d(|H|)$ parametrizing curves $C$ in the…

Let $V$ be a vector bundle over a smooth curve $C$. In this paper, we study twisted Brill--Noether loci parametrising stable bundles $E$ of rank $n$ and degree $e$ with the property that $h^0 (C, V \otimes E) \ge k$. We prove that, under…

The Brill-Noether theory of curves plays a fundamental role in the theory of curves and their moduli and has been intensively studied since the 19th century. In contrast, Brill-Noether theory for higher dimensional varieties is less…

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…

Let X be a ruled surface over a nonsingular curve C of genus $g\geq0$. Let $M_H:=M_{X,H}(2;c_1,c_2)$ be the moduli space of H-stable rank 2 vector bundles E on X with fixed Chern classes $c_i:=c_i(E)$ for $i=1,2$. The main goal of this…

A refined Brill--Noether theory seeks to determine which linear series are admitted by a ``general'' curve in a particular Brill--Noether locus. However, as Brill--Noether loci are not irreducible in general, a coarse answer is given by the…

Let $\M_g$ be the course moduli space of complex projective nonsingular curves of genus $g$. We prove that when the Brill-Noether number $\rho(g,r,n)$ is non-negative every component of the Petri locus $P^r_{g,n}\subset \M_g$ whose general…

Let us consider the locus in the moduli space of curves of genus 2k defined by curves with a pencil of degree k. Since the Brill-Noether number is equal to -2, such a locus has codimension two. Using the method of test surfaces, we compute…

In this paper we consider the Brill-Noether locus $W_{\underline d}(C)$ of line bundles of multidegree $\underline d$ of total degree $g-1$ having a nonzero section on a nodal reducible curve $C$ of genus $g\geq2$. We give an explicit…

Brill-Noether theory studies the existence and deformations of curves in projective spaces; its basic object of study is $\mathcal{W}^r_{d,g}$, the moduli space of smooth genus $g$ curves with a choice of degree $d$ line bundle having at…

Our purpose in this paper is to construct new examples of twisted Brill Noether loci on curves of genus g greater than 2 with negative expected dimension. We begin by completing the proof of Butler's conjecture for coherent systems of…

Let C be a smooth projective algebraic curve of genus g over the finite field F_q. A classical result of H. Martens states that the Brill-Noether locus of line bundles L in Pic^d C with deg L = d and h^0(L) >= i is of dimension at most…

Brill-Noether theory of curves has played a crucial role in the study of curves and their moduli since the 19th century, and has been extensively studied by several authors. Clifford's theorem provides a starting point in determining the…