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15 January 2018 Full-rank affine invariant submanifolds
Maryam Mirzakhani, Alex Wright
Duke Math. J. 167(1): 1-40 (15 January 2018). DOI: 10.1215/00127094-2017-0036

Abstract

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.

Citation

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Maryam Mirzakhani. Alex Wright. "Full-rank affine invariant submanifolds." Duke Math. J. 167 (1) 1 - 40, 15 January 2018. https://doi.org/10.1215/00127094-2017-0036

Information

Received: 23 August 2016; Revised: 25 May 2017; Published: 15 January 2018
First available in Project Euclid: 6 December 2017

zbMATH: 06847241
MathSciNet: MR3743698
Digital Object Identifier: 10.1215/00127094-2017-0036

Subjects:
Primary: 32G15
Secondary: 30F30

Keywords: Abelian differential , affine invariant submanifold , Hodge bundle , rational billiards , Riemann surface , Teichmüller dynamics , translation surface

Rights: Copyright © 2018 Duke University Press

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Vol.167 • No. 1 • 15 January 2018
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