Del Pezzo orders on projective surfaces

In this paper, we generalise the notion of del Pezzo surfaces to orders on surfaces. We show that these del Pezzo orders have del Pezzo centre if the centre is normal Gorenstein and the order has finite representation type. We proceed to classify these del Pezzo orders. The main result is that if the centre is not or the quadric cone, then these del Pezzo orders can be obtained from del Pezzo orders on . Finally, we classify del Pezzo orders on and the quadric cone.