The rationality conjecture for Siegel–Veech area constants

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Let M1{\mathcal M}_1 be a regular SL⁡(2,R)\operatorname{SL}(2,\mathbb R)-invariant suborbifold in a stratum of Abelian differentials, and let carea⁡(M1)c_{\operatorname{area}}({\mathcal M}_1) be its Siegel–Veech area constant. The rationality conjecture for Siegel–Veech constants. The number

π2carea⁡(M1)\pi^2 c_{\operatorname{area}}({\mathcal M}_1)

is rational. This predicts arithmeticity of the normalized area Siegel–Veech constants for all regular invariant suborbifolds; the supplied text does not state whether it has been resolved.

References

Primary source

Alex Eskin, Maxim Kontsevich and Anton Zorich, “Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow”, arXiv:1112.5872 (2013).

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