The WYSIWYG compactification
Abstract
We show that the partial compactification of a stratum of Abelian differentials previously considered by Mirzakhani and Wright is not an algebraic variety. Despite this, we use a combination of algebro-geometric and other methods to provide a short, unconditional proof of Mirzakhani and Wright's formula for the tangent space to the boundary of a GL(2,R) orbit closure, and give new results on the structure of the boundary.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2019
- DOI:
- 10.48550/arXiv.1908.07436
- arXiv:
- arXiv:1908.07436
- Bibcode:
- 2019arXiv190807436C
- Keywords:
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- Mathematics - Dynamical Systems;
- Mathematics - Algebraic Geometry
- E-Print:
- Minor revisions, primarily to sections 7 and 8