Related papers: Non--tautological cycles on Prym moduli spaces

Prym-Teichm\"uller curves $W_D(4)$ constitute the main examples of known primitive Teichm\"uller curves in the moduli space $\mathcal{M}_3$. We determine, for each non-square discriminant $D>1$, the number and type of orbifold points in…

The double ramification cycle satisfies a basic multiplicative relation DRC(a).DRC(b) = DRC(a).DRC(a + b) over the locus of compact-type curves, but this relation fails in the Chow ring of the moduli space of stable curves. We restore this…

After recalling several constructions of the moduli space of curves of genus zero by different people we give our alternative construction of the moduli space. This gives a simple description of the intersection ring of this space. We give…

We describe the moduli space G^r_d of triples consisting of a curve C, a line bundle L on C of degree d, and a linear system V on L of dimension r. This moduli space extends over a partial compactification {\tilde M_g} of M_g inside {\bar…

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 study Shimura curves of PEL type in $\mathsf{A}_g$ generically contained in the Prym locus. We study both the unramified Prym locus, obtained using \'etale double covers, and the ramified Prym locus, corresponding to double covers…

We prove that the locus of Prym curves $(C,\eta)$ of genus $g \geq 5$ for which the Prym-canonical system $|\omega_C(\eta)|$ is base point free but the Prym--canonical map is not an embedding is irreducible and unirational of dimension…

In this paper, we study some aspects of the irreducibility of $\widetilde{M_g^{Pl}(G)}$ and its interrelation with the existence of "normal forms", i.e. non-singular plane equations (depending on a set of parameters) such that a…

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…

Using the theory of Higgs bundles and their stabitlity properties associated to fibered surfaces and the Viehweg-Zuo characterization of Shimura curves in the moduli space of abelian varieties in terms of Higgs bundles, we prove that there…

If the theta-null divisor $\Theta_{\rm null}$ is moved to the Prym moduli space through the diagram $\mathcal{S}_{g}^{+}\rightarrow\mathcal{M}_{g}\leftarrow\mathcal{R}_{g}$, it splits into two irreducible components $\mathcal{P}_{\rm\!…

While there is much work and many conjectures surrounding the intersection theory of the moduli space of curves, relatively little is known about the intersection theory of the Hurwitz space $\mathcal{H}_{k, g}$ parametrizing smooth degree…

We study the topology of the moduli space of unramified $\mathbb{Z}/p$-covers of tropical curves of genus $g \geq 2$, where $p$ is a prime number. We use recent techniques by Chan--Galatius--Payne to identify contractible subcomplexes of…

The Prym map of type (g,n,r) associates to every cyclic covering of degree n of a curve of genus g, ramified at a reduced divisor of degree r, the corresponding Prym variety. We show that the corresponding map of moduli spaces is…

In a previous paper, the authors proved that the Prym variety of any non-cyclic etale triple cover of a smooth curve of genus 2 is a Jacobian variety of dimension 2. This gives a map from the moduli space of such covers to the moduli space…

Let C be a smooth projective complex curve of genus $g\geq2$. We investigate the Brill-Noether locus consisting of stable bundles of rank 2 and canonical determinant having at least $k$ independent sections. Using the Hecke correpondence we…

Curves of genus g which admit a map to CP1 with specified ramification profile mu over 0 and nu over infinity define a double ramification cycle DR_g(mu,nu) on the moduli space of curves. The study of the restrictions of these cycles to the…

Our aim is to determine the tautological algebra generated by the cohomology classes of the Brill-Noether loci in the rational cohomology of the moduli stack $\mathcal{U}_C(n,d)$ of semistable bundles of rank $n$ and degree $d$. We show…

In this paper we prove that the rational Chow rings of $\mathcal{M}_{5,8}$ and $\mathcal{M}_{5,9}$ are tautological, and that these moduli spaces have the Chow K\"unneth generation Property.

We compute the rational Chow ring of the moduli stack of planar nodal curves of fixed degree and express it in terms of tautological classes. Along the way, we extend Vial's results on Chow groups of Brauer-Severi varieties to…