相关论文: The class of the Prym-Brill-Noether divisor

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 define and study the stack ${\mathcal U}^{ns,a}_{g,g}$ of (possibly singular) projective curves of arithmetic genus g with g smooth marked points forming an ample non-special divisor. We define an explicit closed embedding of a natural…

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 ABCT variety is defined as the closure of the image of $G(2,n)$ under the Veronese map. We realize the ABCT variety $V(3,n)$ as the determinantal variety of a vector bundle morphism. We use this to give a recursive formula for the…

In this paper, improving on results of Abramovich- Harris and Debarre- Fahlaoui we give the full classification of curves C of genus g such that a Brill--Noether locus W^ s_d(C), strictly contained in the jacobian J(C) of C, contains a…

Let V^{r}_{d,g, \delta} be the Hilbert scheme of nodal curves in P^r of degree d and arithmetic genus g with \delta nodes. Under suitable numerical assumptions on d and g, for every 0 \le \delta \le g we construct an irreducible component…

Let C be a general element in the locus of curves in M_g lying on some K3 surface, where g is congruent to 3 mod 4 and greater than or equal to 15. Following Mukai's ideas, we show how to reconstruct the K3 surface as a Fourier-Mukai…

The Brill-Noether Theorem gives necessary and sufficient conditions for the existence of a linear series. Here we consider a general n-fold, etale cyclic cover p of a curve C of genus g and investigate for which numbers r,d a linear series…

Let $C$ be a curve of genus $g\geq 2$. A coherent system on $C$ consists of a pair $(E,V)$ where $E$ is an algebraic vector bundle of rank $n$ and degree $d$ and $V$ is a subspace of dimension $k$ of sections of $E$. The stability of the…

In this paper, our aim is to find the relations amongst the cohomology classes of Brill-Noether subvarieties of the moduli space of semistable bundles over an elliptic curve. We obtain results similar to the Poincar\'e relations on a…

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…

We compute the number of moduli of all irreducible components of the moduli space of smooth curves on Enriques surfaces. In most cases, the moduli maps to the moduli space of Prym curves are generically injective or dominant. Exceptional…

Let $X$ be an irreducible smooth projective curve, defined over an algebraically closed field $k$, of genus at least three and $L$ a line bundle on $X$. Let ${\mathcal M}_X(r,L)$ be the moduli space of stable vector bundles on $X$ of rank…

In this paper, we construct some examples of rank-2 Brill-Noether loci with "unexpected" properties on general curves. The key example is in genus 6, but we also have interesting examples in rank 5 and in higher genus. We relate some of our…

The moduli space $\M_{g,n}$ of $n-$pointed stable curves of genus $g$ is stratified by the topological type of the curves being parametrized: the closure of the locus of curves with $k$ nodes has codimension $k$. The one dimensional…

A general curve $C$ of genus six is canonically embedded into the smooth del Pezzo surface $\Sigma \subseteq \mathbb{P}^1 \times \mathbb{P}^2$ of degree $5$ as a divisor in the class $\mathcal{O}_{\Sigma}(2,2)$. In this article, we study…

We construct coarse moduli spaces for `Brill-Noether pairs'. Such a pair consists of a torsion-free sheaf $E$ over an algebraic curve $X$ and a vector subspace $\Lambda$ of its space of sections $H^0(E)$. The construction works for an…

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 approach non-divisorial base loci of big and nef line bundles on irreducible symplectic varieties. While for K3 surfaces, only divisorial base loci can occur, nothing was known about the behaviour of non-divisorial base loci for more…

We produce a lower bound for the dimension of the base locus of the generalized theta divisor on the moduli space SU_C(r) of semistable vector bundles of rank r and trivial determinant on a smooth curve C of genus g > 1.