The boundary of an affine invariant submanifold

The boundary of an affine invariant submanifold We study the boundary of an affine invariant submanifold of a stratum of translation surfaces in a partial compactification consisting of all finite area Abelian differentials over nodal Riemann surfaces, modulo zero area components. The main result is a formula for the tangent space to the boundary. We also prove finiteness results concerning cylinders, a partial converse to the Cylinder Deformation Theorem, and a result generalizing part of the Veech dichotomy. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Inventiones mathematicae Springer Journals

The boundary of an affine invariant submanifold

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2017 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Mathematics, general
ISSN
0020-9910
eISSN
1432-1297
D.O.I.
10.1007/s00222-017-0722-8
Publisher site
See Article on Publisher Site

Abstract

We study the boundary of an affine invariant submanifold of a stratum of translation surfaces in a partial compactification consisting of all finite area Abelian differentials over nodal Riemann surfaces, modulo zero area components. The main result is a formula for the tangent space to the boundary. We also prove finiteness results concerning cylinders, a partial converse to the Cylinder Deformation Theorem, and a result generalizing part of the Veech dichotomy.

Journal

Inventiones mathematicaeSpringer Journals

Published: Feb 22, 2017

References

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