# 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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Filip showed that there are constants $C>0$ and $\delta>0$ such that the number of special Lagrangian fibrations of volume $\leq V$ in a generic twistor family of K3 surfaces is \$C\cdot
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