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… 

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