Counting special Lagrangian fibrations on generic twistor families of K3 surfaces

Resumen:

Partly motivated by a sort of “analogy” between translation and K3 surfaces, Simion Filip extended the classical results of Howard Masur and William Veech for the problem of counting cylinders in translation surfaces by showing that the number N(V) of special Lagrangian fibrations with volume < V on generic twistor families of K3 surfaces is N(V ) = cV 20 + O(V^{20-a}) for some constants c > 0, a > 0. In this talk, we discuss a joint work with Nicolas Bergeron proving that Filip’s theorem is valid for any 0 < a < 4/697633.

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