Related papers: Prym varieties of cyclic coverings
The Prym variety for a branched double covering of a nonsingular projective curve is defined as a polarized abelian variety. We prove that any double covering of an elliptic curve which has more than $4$ branch points is recovered from its…
We study the ramification divisors of projections of a smooth projective variety onto a linear subspace of the same dimension. We prove that the ramification divisors vary in a maximal dimensional family for a large class of varieties.…
We study the $p$-rank stratification of the moduli space of Prym varieties in characteristic $p > 0$. For arbitrary primes $p$ and $\ell$ with $\ell \not = p$ and integers $g \geq 3$ and $0 \leq f \leq g$, the first theorem generalizes a…
To any pair of coverings $f_i: X \ra X_i, i = 1,2$ of smooth projective curves one can associate an abelian subvariety of the Jacobian $J_X$, the Prym variety $P(f_1,f_2)$ of the pair $(f_1,f_2)$. In some cases we can compute the type of…
We study Shimura (special) subvarieties in the moduli space $A_{p,D}$ of complex abelian varieties of dimension $p$ and polarization type $D$. These subvarieties arise from families of covers compatible with a fixed group action on the base…
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 consider unramified coverings of the moduli space $\mathcal{M}_g$ of smooth projective complex curves of genus $g$. Under some hypothesis on the branch locus of the finite extended map to the Deligne-Mumford…
After Jacobians of curves, Prym varieties are perhaps the next most studied abelian varieties. They turn out to be quite useful in a number of contexts. For technical reasons, there does not appear to be any systematic treatment of Prym…
In the moduli space $\mathcal{R}_g$ of double \'etale covers of curves of a fixed genus $g$, the locus formed by covers of curves with a semicanonical pencil consists of two irreducible divisors $\mathcal T^e_g$ and $\mathcal T^o_g$. We…
A new relation between Prym varieties of arbitrary morphisms of algebraic curves and integrable systems is discovered. The action of maximal commutative subalgebras of the formal loop algebra of GL(n) defined on certain infinite-dimensional…
Given a possibly reducible and non-reduced spectral cover X over a smooth projective complex curve C we determine the group of connected components of the Prym variety Prym(X/C). As an immediate application we show that the finite group of…
Given a variety $Y$ with a rectangular Lefschetz decomposition of its derived category, we consider a degree $n$ cyclic cover $X \to Y$ ramified over a divisor $Z \subset Y$. We construct semiorthogonal decompositions of $\mathrm{D^b}(X)$…
We consider maps on genus-$g$ surfaces with $n$ (labeled) faces of prescribed even degrees. It is known since work of Norbury that, if one disallows vertices of degree one, the enumeration of such maps is related to the counting of lattice…
We compute the twisted cohomology of the mapping class group with level structures, with coefficients in the $r$-tensor powers of the Prym representations for any positive integer $r$. When $r\ge 2$, we show that the cohomology exhibits…
We classify homomorphisms from the braid group on $n$ strands to the pure mapping class group of a nonoriantable surface of genus $g$. For $n\ge 14$ and $g\le 2\lfloor{n/2}\rfloor+1$ every such homomorphism is either cyclic, or it maps…
We construct configuration spaces for cyclic covers of the projective line that admit extra automorphisms and we describe the locus of curves with given automorphism group. As an application we provide examples of arbitrary high genus that…
In this note, we introduce the notion of an unramified strongly cyclic covering for a cyclic curve, a class that has similar properties to, and contains, unramified double covers of hyperelliptic curves. We determine several of their basic…
Let F^N_g be the moduli space of polarized Nikulin surfaces (Y,H) of genus g and let P^N_g be the moduli of triples (Y,H,C), with C in |H| a smooth curve. We study the natural map \chi_g:P^N_g -> R_g, where R_g is the moduli space of Prym…
In the moduli space $\mathcal{R}_g$ of double \'etale covers of curves of a fixed genus $g$, the locus of covers of curves with a semicanonical pencil decomposes as the union of two divisors $\mathcal{T}^e_g$ and $\mathcal{T}^o_g$. Adapting…
We consider the space $\mathcal R_{g,S_3}^{S_3}$ of curves with a connected $S_3$-cover, proving that for any odd genus $g\geq 13$ this moduli is of general type. Furthermore we develop a set of tools that are essential in approaching the…