Related papers: Refined Brill-Noether theory for all trigonal curv…
We study the Brill-Noether theory of curves on K3 surfaces that are Hodge theoretically associated to cubic fourfolds of discriminant 14. We prove that any smooth curve in the polarization class has maximal Clifford index and deduce that a…
A Laurent polynomial $f$ in two variables naturally describes a projective curve $C(f)$ on a toric surface. We show that if $C(f)$ is a smooth curve of genus at least 7, then $C(f)$ is not Brill-Noether general. To accomplish this, we…
In this paper, we study maps from reducible curves $f : C \cup_\Gamma D \to \mathbb{P}^r$. We restrict our attention to two cases: first, when $f|_D$ factors through a hyperplane $H$ and $f|_C$ is transverse to $H$; and second, when $r =…
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…
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…
We construct pointed Prym-Brill-Noether varieties parametrizing line bundles assigned to an irreducible \'etale double covering of a curve with a prescribed minimal vanishing at a fixed point. We realize them as degeneracy loci in type D…
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…
We attempt to describe the rank 2 vector bundles on a curve C which are specializations of the trivial bundle. We get a complete classifications when C is Brill-Noether generic, or when it is hyperelliptic; in both cases all limit vector…
In this paper we determine the number of general points through which a Brill--Noether curve of fixed degree and genus in any projective space can be passed.
The geometry of Sp(3)/U(3) as a subvariety of Gr(3,6) is explored to explain several examples given by Mukai of non-abelian Brill-Noether loci, and to give some new examples. These examples identify Brill-Noether loci of vector bundles on…
We extend a result by Fulton-Harris-Lazarsfeld in Brill-Noehter theory of line bundles and, as well, a result by Aprod-Sernesi in theory of Secant Loci, to the Brill-Noehter locus of stable bundles inside the moduli space of higher rank…
We provide a bound on the $\Theta$-regularity of an arbitrary reduced and irreducible curve embedded in a polarized abelian variety in terms of its degree and codimension. This is an "abelian" version of Gruson-Lazarsfeld-Peskine's bound on…
We briefly survey recent results related to linear series on curves that are general in various moduli spaces, highlighting the interplay between algebraic geometry on a general curve and the combinatorics of its degenerations.…
We use the Brill-Noether theory to prove the Green conjecture for exceptional curves on K3 surfaces. Such curves count among the few ones having Clifford dimension at least three. We obtain our result by adopting an infinitesimal approach…
In this paper we consider the singularities of the varieties parameterizing stable vector bundles of fixed rank and degree with sections on a smooth curve of genus at least two. In particular, we extend results of Y. Laszlo, and of the…
We initiate the study of Prym-Brill-Noether theory for ramified double covers, extending several key results from classical Prym-Brill-Noether theory to this new framework. In particular, we improve Kanev's results on the dimension of…
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 prove a non abelian Torelli type result for smooth projective curves by working in the derived category of some associated polarized Quot schemes and defining Brill-Noether loci and Abel-Jacobi maps on them.
Using limit linear series on chains of curves, we show that closures of certain Brill--Noether loci contain a product of pointed Brill--Noether loci of small codimension. As a result, we obtain new non-containments of Brill--Noether loci,…
Given the Prym variety of an \'etale double cover one can define analogues of the classical Brill-Noether loci on Jacobians of curves. Recent work by Lahoz and Naranjo shows that the Brill-Noether locus $V^2$ completely determines the…