Teichmüller curves in genus two: Discriminant and spin

By Curtis T. McMullen. 2005

210 citations recorded by the source corpus.

Subfields: Computational Mechanics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/9309eed35c001a321eff50d16903f9f5725c560d

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In Computational Mechanics

In Geometry and Topology

Citations in the corpus

Teichmüller curves in genus two: Torsion divisors and ratios of sines (2006, methodology): “Figure 4. The prototypical form of type (a,b,c,e) and width t. By [ Mc3 , §1 and Cor.”
Splitting mixed Hodge structures over affine invariant manifolds (2013, methodology): “Note that the “spin” invariant used by McMullen [McM05] to distinguish them is thus not Galois invariant.”
Prym Varieties and Teichmüller Curves (2006, background): “Classification. The primitive Teichm¨uller curves in genus 2 are classified in [ Mc2 ] and [Mc4]; in particular, it is shown (using [Mo]) that there is only one such curve lying outside S WD ⊂ M2. It would be interesting to have”
A criterion for the simplicity of the Lyapunov spectrum of square-tiled surfaces (2013, unknown): “, [2,13,24,28,37,38,51], and references therein.”
Introduction to Teichm\"uller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards (2013, background): “McMullen [66], it is possible to show that the SL(2,Z)-orbits of origamis are organized as follows”
Braid groups and Hodge theory (2013, methodology): “ρr(Bn). The locus F(Z) ⊂ S is a Kobayashi geodesic subvariety, reminiscent of the Teichm¨uller curves on Hilbert modular surfaces studied in [Mc1] and [ Mc2 ].”
Veech groups without parabolic elements (2005, background): “See say [KS], [MT], [Mc1, Mc2], [T], [Ve2] for more details; See also [ Mc3 , Mc4, Mc5], for recent related developments.”
Prime arithmetic Teichmüller discs in $$\mathcal{H}(2)$$ (2004, background): “By [ Mc2 ], for even n all these surfaces are in the same orbit, and for odd n > 5 they fall into two orbits.”
On the minimum dilatation of pseudo-Anosov homeomorphisms on surfaces of small genus (2009, methodology): “We also summarizes basic tools for proving our results (for example see [28, 9, 22, 23]).”
Periodic points on Veech surfaces and the Mordell-Weil group over a Teichmüller curve (2004, background): “In contrast to that, the stratum ΩM2(2) contains infinitely many Teichmuller curves that are not obtained via torus coverings (see [ McM05a ]).”
Teichmüller curves in genus two: The decagon and beyond (2005, unknown): “(Note that jPDj is the same as the number of cusps of the Weierstrass curve WD [Mc4], Cor.”