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

We prove that in characteristic p>0 the locus of stable curves of p-rank at most f is pure of codimension g-f in the moduli space of stable curves. Then we consider the Prym map and analyze it using tautological classes. We study the locus…

In this paper we prove that the Prym map, from the space of double coverings of a curve of genus g with r branch points to the moduli space of abelian varieties, is generically injective if r>6 and g>1, r=6 and g>2, r=4 and g>4, r=2 and…

Let $\mathcal{I}_{d,g,R}$ be the union of irreducible components of the Hilbert scheme whose general points parametrize smooth, irreducible, curves of degree $d$, genus $g$, which are non--degenerate in the projective space $\mathbb{P}^R$.…

In this paper we introduce and study divisorial (i) classes} for the blow up of projective space in several points for i=-1,0 and 1. We generalize Noether's inequality, and we prove that all divisorial (i) classes are in bijective…

In this paper we investigate generalized theta divisors $\Theta_r$ in the moduli spaces $\mathcal{U}_C(r,r)$ of semistable vector bundles on a curve $C$ of genus $2$. We provide a desingularization $\Phi$ of $\Theta_r$ in terms of a…

We study the Noether-Lefschetz locus of the moduli space $\mathcal{M}$ of $K3^{[2]}$-fourfolds with a polarization of degree $2$. Following Hassett's work on cubic fourfolds, Debarre, Iliev, and Manivel have shown that the Noether-Lefschetz…

In the paper we consider the Jacobian locus $\overline{J_g}$ and the Prym locus $\overline{P_{g+1}}$, in the moduli space $A_g$ of principally polarized abelian varieties of dimension $g$, for $g\geq 7$, and we study the extrinsic geometry…

This article is a generalisation of results of Ciliberto and Sernesi. For a general canonically embedded curve $C$ of genus $g\geq 5$, let $d\le g-1$ be an integer such that the Brill--Noether number $\rho(g,d,1)=g-2(g-d+1)\geq 1$. We study…

In the moduli space $\mathcal{C}$ of complex cubic hypersurfaces $X\subset\mathbb{P}^5$, we study the condition that $X$ admits a net of polar quadrics whose discriminant locus is a $10$-nodal irreducible plane sextic curve. Our main result…

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…

We prove that the normal bundle of a general Brill-Noether curve of genus $g \geq 1$ and degree $d$ in $\mathbb{P}^r$ is semistable if $g=1$ or $g\geq \left \lceil \frac{5r}{2}\right\rceil r(r-1)$, or $d$ is larger than an explicit function…

For a generic compact Riemann surface the theta function is at every point on the Jacobian equal to its first Taylor term, up to a holomorphic change of local coordinates and multiplication by a local holomorphic unit. More generally, any…

In this note we give an easy proof of the existence of generically smooth components of the expected dimension of certain Brill--Noether loci of stable rank 2 vector bundles on a curve with general moduli, with related applications to…

We study the conormal geometry theta divisors of certain singular bielliptic curves. We apply these results to the boundary components $\mathscr{S}_\underline{d}$ of the bielliptic Prym locus. We obtain results on the Gauss map, compute the…

Generalizing the Martens theorem for line bundles over a curve $C$, we obtain upper bounds on the dimension of the Brill--Noether locus $B^k_{n, d}$ parametrizing stable bundles of rank $n \ge 2$ and degree $d$ over $C$ with at least $k$…

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…

A Brill-Noether degeneracy locus is closure in $\Pic^d(C)$ of the locus of line bundles with a specified rank function $r(a,b) = h^0(C,L(-ap-bq))$. These loci generalize the classical Brill-Noether loci $W^r_d(C)$ as well as Brill-Noether…

We study some natural linear systems carried by polarized Nikulin surfaces of genus g. We determine their positivity and establish their Brill-Noether theory. As an application, we compute the class of some natural effective divisors…

We study moduli spaces of K3 surfaces endowed with a Nikulin involution and their image in the moduli space R_g of Prym curves of genus g. We observe a striking analogy with Mukai's well-known work on ordinary K3 surfaces. Many of Mukai's…

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…