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

1. Hom(E,E)=C
2. Ext^2(E,E)=C 3 Ext^i=0 otherwise.

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

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?