Spherical objects $E$ in the derived category of coherent sheaves over a K3 surface satisfy:

- $\operatorname{Hom}(E,E)=\mathbb{C}$,
- $\operatorname{Ext}^2(E,E)=\mathbb{C}$,
- $\operatorname{Ext}^i(E,E)=0$ otherwise.

Are the structure sheaf $O_X$ and the sheaves associated with the exceptional divisors the only spherical objects on a Kummer surface?