On special Lagrangian fibrations in generic twistor families of K3 surfaces

Nicolas Bergeron (1) , Carlos Matheus (2)

1 UPMC - Université Pierre et Marie Curie - Paris 6
2 LAGA - Laboratoire Analyse, Géométrie et Applications

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 $0<\delta<\frac{4}{697633}$.

Domaines: Mathématiques [math]; Systèmes dynamiques [math.DS]; Géométrie algébrique [math.AG]

Nicolas Bergeron, Carlos Matheus. On special Lagrangian fibrations in generic twistor families of K3 surfaces. Annales Scientifiques de l'École Normale Supérieure, 2020, 53 (3), pp.740-750. ⟨hal-02414021⟩