Vorträge in der Woche 07.07.2025 bis 13.07.2025

Mittwoch, 09.07.2025: The tropical Donagi theorem

Thomas Saillez (Université Libre de Bruxelles)

In tropical geometry, we have a lot of analogues of theorems from algebraic geometry. The aim of this talk is to discuss the tropical analogy of the tetragonal construction, which is a combinatorial construction used in the study of abelian varieties. Under reasonable assumptions, the tetragonal construction associates to the data of a double cover of a quadruple cover of a curve two other pairs of such covers. A remarkable result is that indeed it forms a triality of pairs of covers (applying the construction to one pair of covers outputs the other two) and that the Prym varieties, a generalization of Jacobians arising from double covers, are isomorphic. We are going to introduce those elements in the context of tropical geometry and explore the results we can obtain there.