The field of definition of affine invariant submanifolds of the moduli space of abelian differentials
By A. Wright. 2012
79 citations recorded by the source corpus.
The field of definition of an affine invariant submanifold M is the smallest subfield of R such that M can be defined in local period coordinates by linear equations with coefficients in this field. We show that the field of definition is equal to the intersection of the holonomy fields of translation surfaces in M, and is a real number field of degree at most the genus. We show that the projection of the tangent bundle of M to absolute cohomology H 1 is simple, and give a direct sum decomposition of H 1 analogous to that given by Moller in the case of Teichmuller curves. Applications include explicit full measure sets of translation surfaces whose orbit closures are as large as possible, and evidence for finiteness of algebraically primitive Teichmuller curves. The proofs use recent results of Avila, Eskin, Mirzakhani, Mohammadi and Moller. 32G15, 37D40
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/82d3ed1a33649818ee9bd745a54080c1cd469ec6
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In Applied Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Cylinder deformations in orbit closures of translation surfaces (2013, background): “On the other hand, Mirzakhani conjectures (see Wright [29]) that any orbit closure M that does not arise from a covering construction must satisfy dimC p.T .”