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Full-rank affine invariant submanifolds
Maryam Mirzakhani, Alex Wright
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Source: Crossref
Published: Jan 15, 2018
DOI: 10.1215/00127094-2017-0036
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We show that every GL(2,R) orbit closure of translation surfaces is 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.
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