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arXiv · 1608.02147

Full rank affine invariant submanifolds

Maryam Mirzakhani·Alex Wright
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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.

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Maryam Mirzakhani, Alex Wright. 2016-08-06. Full rank affine invariant submanifolds. https://doi.org/10.1215/00127094-2017-0036

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