Abstract for the talk on 26.07.2017 (10:00 h)Group Seminar
Martin Ulirsch (MPI MIS, Leipzig)
Realizability of tropical abelian differentials
The realizability problem for tropical abelian differentials can be stated as follows: Given a pair (Γ,D) consisting of a stable tropical curve Γ and a divisor D in the canonical linear system on Γ, we give a purely combinatorial condition to decide whether there is a smooth curve realizing Γ 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.