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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… Click to show full abstract
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.
Keywords:
affine invariant;
rank affine;
full rank;
invariant submanifolds
Journal Title: Duke Mathematical Journal
Year Published: 2018
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Journal Title: Duke Mathematical Journal
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!