Geometry of Brill-Noether loci on prym varieties

On the Cohomology of Brill-noether Loci over Quot Schemes

Let C be a smooth projective irreducible curve over an algebraic closed field k of characteristic 0. We consider Brill-Noether loci over the moduli space of morphisms from C to a Grassmannian G(m, n) of m−planes in k and the corresponding Quot schemes of quotients of a trivial vector bundle on C compactifying the spaces of morphisms. We study in detail the case in which m = 2, n = 4. We prove r...

Brill-noether Geometry on Moduli Spaces of Spin Curves

The aim of this paper is to initiate a study of geometric divisors of Brill-Noether type on the moduli space Sg of spin curves of genus g. The moduli space Sg is a compactification the parameter space Sg of pairs [C, η], consisting of a smooth genus g curve C and a theta-characteristic η ∈ Pic(C), see [C]. The study of the birational properties of Sg as well as other moduli spaces of curves wit...

Brill - Noether Loci and the Fourier - Mukai Transform

Theta-regularity of Curves and Brill–noether Loci

We provide a bound on the Θ-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 the Castelnuovo–Mumford regularity of a non-degenerate curve embedded in a projective space. As an application, we provide a Castelnuovo type bound for the genus o...

0 Brill - Noether Loci and the Gonality Stratification of M

For an irreducible smooth projective complex curve C of genus g, the gonality defined as gon(C) = min{d ∈ Z≥1 : there exists a gd on C} is perhaps the second most natural invariant: it gives an indication of how far C is from being rational, in a way different from what the genus does. For g ≥ 3 we consider the stratification of the moduli space Mg of smooth curves of genus g given by gonality:...