On cascades of log del Pezzo surfaces

A normal projective surface with quotient singularities is called a log del Pezzo surface if the anticanonical divisor is ample. There have been extensive work devoted to classify log del Pezzo surfaces.To achieve this goal, we proposed an approach by using the concept of a 'cascade', which can be viewed as a generalization of the classification of the smooth del Pezzo surfaces. So far this approach has been reasonably successful in the case when the log del Pezzo surface is toric or is of Picard number one.

In this talk, I will briefly review the known classification of log del Pezzo surfaces and explain how our approach leads to the classification. Some application of this approach relies on computing power. If time permit, I will mention a web-based computer program realizing this approach.