2016/08/31 by Maryam Mirzakhani, Alex Wright · 1 citation
Mathematics · #math.DS #math.AG
paper · pdf · doi:10.1215/00127094-2017-0036
published as Duke Math. J. 167, no. 1 (2018), 1-40 · minor update; final version
arxiv created 2017/10/22 · arxiv updated 2018/02/21
We show that every GL(2, R) orbit closure of translation surfaces is either a connected component of a stratum, the hyperelliptic locus, or consists entirely of surfaces whose Jacobians have extra endomorphisms. We use this result to give applications related to polygonal billiards. For example, we exhibit infinitely many rational triangles whose unfoldings have dense GL(2,R) orbit.