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Irene Spelta

Publications and source records attributed to Irene Spelta.

9 recordsLinked to original sources
arXiv2026

Genus three Ceresa cycles and limit of archimedean heights

For a one-parameter variation of biextension mixed Hodge structures, Brosnan and Pearlstein showed that the limit of the asymptotic height of the variation is given by a certain limit height of the nilpotent orbit. This limit height depends on the choice of a parameter. In the case of a variation of geometric origin related to Ceresa cycles associated with curves of genus three, after fixing a parameter, we show that this limit height is given by the Deligne splitting of a biextension mixed Hodge structure associated with cycles in the boundary.

math.AG↗
arXiv2025

Families of cyclic curve coverings with maximal monodromy

We study the algebraic monodromy of families of cyclic Galois coverings of curves. Under a condition on the $G$-decomposition of the associated variation of Hodge structures, we prove a criterion for the maximality of the monodromy. The proof combines the genus-zero case with a degeneration argument involving Prym varieties of certain admissible coverings. As a consequence of our criterion, we show that for $g\geq 8$ there exists no special family of Galois covers of the type we consider, providing new evidence towards the Coleman-Oort conjecture. Finally, we determine when the loci of double and triple Galois covers are totally geodesic.

math.AG↗
arXiv2024

Monodromy of the Prym map and semicanonical pencils in genus 6

The Prym map $\mathcal{P}_6$ in genus 6 is dominant and generically finite of degree 27. When restricted to the divisor of curves with an odd semicanonical pencil $\mathcal{T}_6^o$, it is still generically finite, but of degree strictly smaller. In this paper, we prove that $\mathcal{P}_6$ restricted to $\mathcal{T}_6^o$ is birational and that the monodromy group over the image of $\mathcal{T}_6^o$ is the Weyl group $WD_5$. Thus, there are two other irreducible divisors in the moduli space of Prym curves $\mathcal{R}_6$ and the degree of $\mathcal{P}_6$ restricted to them is 10 and 16. Moreover, we study the geometry of the divisor where $\mathcal{P}_6$ has degree 10.

math.AG↗
arXiv2023

Gauss-Prym maps on Enriques surfaces

We prove that the $k$-th Gaussian map $γ^k_{H}$ is surjective on a polarized unnodal Enriques surface $(S, H)$ with $ϕ(H)>2k+4$. In particular, as a consequence, when $ϕ(H)>4(k+2)$, we obtain the surjectivity of the $k$-th Gauss-Prym map $γ^k_{ω_C\otimesα}$ on smooth hyperplane sections $C\in \vert H\vert.$ In case $k=1$ it is sufficient to ask $ϕ(H)>6$.

math.AG↗
arXiv2023

Decomposable abelian $G$-curves and special subvarieties

We consider families of abelian Galois coverings of the line. When the Jacobian of the general element is totally decomposable, i.e., is isogenous to a product of elliptic curves, we prove that they yield special subvarieties of $\A_g$ if and only if a numerical condition holds, which in the general case is only known to be sufficient.

math.AG↗
arXiv2021

Explicit analysis of positive dimensional fibres of $ \mathcal{P}_{g,r} $ and Xiao conjecture

We focus on the positive dimensional fibres of the Prym map $\mathcal{P}_{g,r}$. We present a direct procedure to investigate infinitely many examples of positive dimensional fibres. Such procedure uses families of Galois coverings of the line admitting a 2-sheeted Galois intermediate quotient. Then we generalize to families of Galois coverings of the line admitting a Galois intermediate quotient of higher degree and we show that the higher degree analogue of the aforementioned procedure gives all the known counterexamples to a conjecture by Xiao on the relative irregularity of a fibration.

math.AG↗
arXiv2021

Shimura subvarieties via endomorphisms

We show the existence of two new Shimura subvarieties of $\mathcal{A}_2, \mathcal{A}_3$ generically contained in the Torelli locus. They provide the first examples of Shimura subvarieties obtained by means of Jacobians carrying non-trivial endomorphisms not directly induced by the automorphisms of the curves. We also obtain a new example of a Shimura subvariety of $\mathcal{A}_4$ generically contained in the Prym locus.

math.AG↗
arXiv2020

Infinitely many Shimura varieties in the Jacobian locus for $g \leq 4$

We study families of Galois covers of curves of positive genus. It is known that under a numerical condition these families yield Shimura subvarieties generically contained in the Jacobian locus. We prove that there are only 6 families satisfying this condition, all of them in genus 2,3 or 4. We also show that these families admit two fibrations in totally geodesic subvarieties, generalizing a result of Grushevsky and Möller. Countably many of these fibres are Shimura. Thus the Jacobian locus contains infinitely many Shimura subvarieties of positive dimension of any $g \leq 4$.

math.AG↗