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- W3039153670 abstract "The number of closed billiard trajectories in a rational-angled polygon grows quadratically in the length. This paper gives an analogue on K3 surfaces, by considering special Lagrangian tori. The analogue of the angle of a billiard trajectory is a point on a twistor sphere, and the number of directions admitting a special Lagrangian torus fibration with volume bounded by $ V $ grows like $ V^{20} $ with a power-saving term. Bergeron--Matheus have explicitly estimated the exponent of the error term as $ {20-frac{4}{697633} }$. The counting result on K3 surfaces is deduced from a count of primitive isotropic vectors in indefinite lattices, which is in turn deduced from equidistribution results in homogeneous dynamics." @default.
- W3039153670 created "2020-07-10" @default.
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- W3039153670 date "2020-01-01" @default.
- W3039153670 modified "2023-09-27" @default.
- W3039153670 title "Counting special lagrangian fibrations in twistor families of K3 surfaces" @default.
- W3039153670 doi "https://doi.org/10.24033/asens.2432" @default.
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