## View abstract

### Session S35 - Moduli Spaces in Algebraic Geometry and Applications

Thursday, July 15, 13:20 ~ 14:00 UTC-3

## Global Prym-Torelli theorem for ramified double coverings

### Angela Ortega

In this talk we will give an introduction to the Prym varieties and the Prym maps. We will then consider the Prym map between the moduli space $\mathcal{R}_{g,r}$ of double coverings over a genus g curve ramified at r points and $\mathcal{A}^{\delta}_{g-1+r/2}$ the moduli space of polarised abelian varieties of dimension $g-1+r/2$ with polarisation of type $\delta$. Unexpectedly, in the ramified case the Prym map is everywhere an embedding when $r \geq 6$ and $g>0$. We will present a constructive proof of this result.