Classification of Canonical Del Pezzo Orders

We classify del Pezzo non-commutative surfaces that are finite over their centres and have no worse than canonical singularities. Using the minimal model program, we introduce the minimal model of such surfaces. We first classify the minimal models and then give the classification of these surfaces in general. This presents a complementary result and method to the classification of del Pezzo orders over projective surfaces given by Chan and Kulkarni in 2003