arXiv 1608.021472016-08math.DSmath.AG

Full rank affine invariant submanifolds

Maryam Mirzakhani, Alex Wright

备注：: minor update; final version
发表信息：: Duke Math. J. 167, no. 1 (2018), 1-40
DOI：: 10.1215/00127094-2017-0036

英文摘要：

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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