Dr. Giusi Capobianco: Algebraic and tropical Prym-Torelli map

Abstract: Given an étale double cover of smooth curves one can associate a principally polarized abelian variety called the Prym variety. The map from the moduli space of double covers Rg to the moduli space of pp abelian varieties Ag-1 is called Prym-Torelli, in analogy with the Jacobian case. This map does not extend to a morphism from the boundary of Rg to any of the standard toroidal compactifications of Ag-1. In this talk I will present their tropical counterpart and prove that, with a slight modification of the definition, the tropical Prym-Torelli map is continuous.
This result is part of my PhD thesis and will appear on the arXiv soon.