Exceptional sheaves on the Hirzebruch surface $\mathbb{F}_2$

The structures of exceptional objects on Del Pezzo surfaces are completely determined by Kuleshov and Orlov. On the other hand, the structure of exceptional objects on weak Del Pezzo surfaces are much more complicated by the existence of -2-curves. We study the structure of exceptional sheaves on the Hirzebruch surface with a -2-curve, the easiest example of weak Del Pezzo surfaces. My talk is based on a joint work with Shinnosuke Okawa.