Exceptional bundles and Q-Gorenstein degeneration of surfaces
In this talk, I would like to explain our recent results and progress on the exceptional bundles associated with Q-Gorenstein degeneration of surfaces. The technical motivation is due to the result of Hacking, which gives the construction of exceptional bundles when the underlying surface has a Q-Gorenstein degeneration to a singularity of class T_1. We briefly introduce his construction, and discuss an extension to the surfaces having degenerations to singularities of class T_d. As an application, I introduce the relation to the three block exceptional collections of del Pezzo surfaces. If time permits, I will also introduce another application to the construction of exceptional collections in algebraic surfaces with p_g=q=0.