Realizability of tropical abelian differentials

  • Martin Ulirsch (MPI MiS, Leipzig)
E1 05 (Leibniz-Saal)


The realizability problem for tropical abelian differentials can be stated as follows: Given a pair $(\Gamma, D)$ consisting of a stable tropical curve $\Gamma$ and a divisor $D$ in the canonical linear system on $\Gamma$, we give a purely combinatorial condition to decide whether there is a smooth curve realizing $\Gamma$ together with a canonical divisor that specializes to $D$. In this talk I am going to introduce the basic notions needed to understand this problem and outline a comprehensive solution based on recent work of Bainbridge-Chen-Gendron-Grushevsky-Möller on compactifcations of strata of abelian differentials. Along the way, I will also develop a moduli-theoretic framework to understand the specialization of divisors to tropical curves as a natural tropicalization map in the sense of Abramovich-Caporaso-Payne.

This talk is based on joint work with Bo Lin, as well as on an ongoing project with Martin Möller and Annette Werner.

Katharina Matschke

MPI for Mathematics in the Sciences Contact via Mail