Prime arithmetic Teichmüller discs in $$\mathcal{H}(2)$$
By Pascal Hubert, Samuel Lelièvre. 2004
87 citations recorded by the source corpus.
It is well-known that Teichmüller discs that pass through “integer points” of the moduli space of abelian differentials are very special: they are closed complex geodesics. However, the structure of these special Teichmüller discs is mostly unexplored: their number, genus, area, cusps, etc.We prove that in genus two all translation surfaces in $$\mathcal{H}(2)$$ tiled by a prime number n > 3 of squares fall into exactly two Teichmüller discs, only one of them with elliptic points, and that the genus of these discs has a cubic growth rate in n.
Subfields: Geometry and Topology, Mathematical Physics, Theoretical Computer Science
View Paper: https://www.semanticscholar.org/paper/1ab4e12c77532ea4548ecb8e220eb8b778300f07
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In Geometry and Topology
- Carlos Matheus
- J. Yoccoz
- Martin Möller
- Gabriela Schmithuesen
- Frank Herrlich
- G. Forni
- A. Zorich
- Curtis T. McMullen
In Mathematical Physics
- Carlos Matheus
- J. Yoccoz
- Martin Möller
- Gabriela Schmithuesen
- Frank Herrlich
- A. Zorich
- Marcelo Viana
- G. Forni
In Theoretical Computer Science
Citations in the corpus
- A criterion for the simplicity of the Lyapunov spectrum of square-tiled surfaces (2013, methodology): “Following the work of Kani [29] and Hubert–Lelièvre [28] in genus two, it is natural to partition the fixed points of ι in the followingway.”
- On the boundary of Teichmüller disks in Teichmüller and in Schottky space (2007, background): “Origamis in genus 2 where q has one zero are classified in [19].”
- An extraordinary origami curve (2005, background): “Some interesting facts about origamis are contained e.g. in [ HL ] and [M1].”