2020/03/04 by Thomas Le Fils, Fils, Thomas Le
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2003.02216
openalex publication_date 2020/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a necessary and sufficient condition for a representation of the fundamental group of a closed surface of genus at least 2 to \mathbb C to be the holonomy of a translation surface with a prescribed list of conical singularities. Equivalently, we determine the period maps of abelian differentials with prescribed list of multiplicites of zeros. Our main result was also obtained, independently, by Bainbridge, Johnson, Judge and Park.