# On special Lagrangian fibrations in generic twistor families of K3 surfaces

## TL;DR

This paper refines the understanding of the distribution of special Lagrangian fibrations in generic twistor families of K3 surfaces, providing a more precise error term in their counting formula.

## Contribution

It improves the error estimate in the asymptotic count of special Lagrangian fibrations, showing that the decay rate can be arbitrarily close to zero.

## Key findings

- The number of fibrations grows as a constant times V^{20}.
- The error term can be made arbitrarily small, specifically any positive number less than 4/697633.
- The result enhances the precision of asymptotic counts in geometric analysis of K3 surfaces.

## Abstract

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 $C\cdot V^{20}+O(V^{20-\delta})$. In this note, we show that $\delta$ can be taken to be any number $0<\delta<\frac{4}{697633}$.