Related papers: Geometry of Brill-Noether loci on Prym varieties

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…

Mukai showed that projective models of Brill-Noether general polarized K3 surfaces of genus $6-10$ and $12$ are obtained as linear sections of projective homogeneous varieties, and that their hyperplane sections are Brill-Noether general…

We prove that the pullbacks of the virtual fundamental classes of the Brill-Noether loci under any Abel-Jacobi section lie in the tautological ring of the moduli space of stable curves. This resolves a conjecture of Pagani, Ricolfi and van…

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…

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…

In this manuscript we sharpen the lower bound on the codimension of the irreducible components of the Noether-Lefschetz locus of surfaces in projective toric threefolds given in [BG17]. We also provide a simpler proof of Theorem 4.11 in…

Let $\pi: X \longrightarrow C$ be a fibration with reduced fibers over a curve $C$ and consider a polarization $H$ on the surface $X$. Let $E$ be a stable vector bundle of rank $2$ on $C$. We prove that the pullback $\pi^*E$ is a $H-$stable…

It is known that the Jacobian of an algebraic curve which is a 2-fold covering of a hyperelliptic curve ramified at two points contains a hyperelliptic Prym variety. Its explicit algebraic description is applied to some of the integrable…

In this paper, we consider Abelian varieties over function fields that arise as twists of Abelian varieties by cyclic covers of irreducible quasi-projective varieties. Then, in terms of Prym varieties associated to the cyclic covers, we…

Let $P \cup P'$ be the two component Prym variety associated to an \'etale double cover $\tilde{C} \to C$ of a non-hyperelliptic curve of genus $g \geq 6$ and let $|2\Xi_0|$ and $|2\Xi_0'|$ be the linear systems of second order theta…

We prove a generalization of the Brill-Noether theorem for the variety of special divisors $W^r_d(C)$ on a general curve $C$ of prescribed gonality. Our main theorem gives a closed formula for the dimension of $W^r_d(C)$. We build on…

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…

It is shown that the map from the Jacobian of the spectral curve to the moduli of stable bundles of rank 2 is generically simply branched along an irreducible divisor. This observation falsifies the key step in the "abelianization of the…

We study the cohomology of a general stable sheaf on an abelian surface. We say that a moduli space satisfies weak Brill-Noether if the general sheaf has at most one non-zero cohomology group. Let $(X,H)$ be a polarized abelian surface and…

Given a vector bundle $V$ over a curve $X$, we define and study a surjective rational map $\mathrm{Hilb}^d (\mathbb{P} V ) - \mathrm{Quot}^{0, d} ( V^* )$ generalising the natural map $\mathrm{Sym}^d X \to \mathrm{Quot}^{0, d} ({\mathcal…

We describe the isotypical decomposition of the Jacobian variety JW of the Galois extension W-->T of any fourfold cover of smooth connected irreducible projective complex curves X-->T, in terms of Prym's of intermediate covers. We also…

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…

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…

We prove that the extension of the double ramification cycle defined by the first-named author (using modifications of the stack of stable curves) coincides with that defined by the last-two named authors (using an extended Brill-Noether…

Let P^2_r be the projective plane blown up at r generic points. Denote by E_0,E_1,...,E_r the strict transform of a generic straight line on P^2 and the exceptional divisors of the blown-up points on P^2_r respectively. We consider the…