• DOI:10.24033/asens.2432
• Corpus ID: 119646804

Counting special lagrangian fibrations in twistor families of K3 surfaces

@article{Filip2016CountingSL,
  title={Counting special lagrangian fibrations in twistor families of K3 surfaces},
  author={Simion Filip},
  journal={Annales scientifiques de l'{\'E}cole normale sup{\'e}rieure},
  year={2016}
}

• Simion Filip
• Published 27 December 2016
• Mathematics
• Annales scientifiques de l'École normale supérieure

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.