Felix
Röhrle
University of Tübingen
Towards the fibers of the tropical Prym-Torelli morphism
Abstract.
Curves and abelian varieties are the most studied classes of algebro-geometric objects. The Torelli morphism relates the two worlds. Since it is injective, this is a strong and valuable tool. Prym varieties generalize Jacobians: they are the natural abelian variety associated to an étale double cover of curves. The Prym-Torelli morphism, however, is never injective.
In this talk I will take the perspective of tropical geometry, where curves become graphs and abelian varieties become symmetric bilinear forms. I present partial results on the structure of the fibers of the tropical Prym-Torelli morphis:
(1) In joint work with Dmitry Zakharov, we have identified positive dimensional fibers. These phenomena are exhibited through a matroidal perspective.
(2) In joint work with Thomas Saillez, we proved an analog of Donagi's theorem. It induces a discrete structure in the fibers.